Bibliographic references
Shchemelev V. I., Ermakov A. I. Wave blade finite element with six node degrees of freedom. Trudy MAI, 2024, no 136 As of today, the problems of dynamic strength of the impellers of any gas turbine engine are solved mainly by the frequency detuning from resonances located near its main operating modes. Frequency detuning can often only be achieved successfully by optimal design. The task of performing frequency detuning becomes significantly more complicated if the rotor impellers significantly affect each other oscillations. In this case, the time required to perform the adjustment, even when employing powerful computers, becomes unacceptably large. One of the options for solving this problem is to application of methods for computing vibrations of impellers that are more efficient in terms of computational performance. These include the wave finite element method. A wave blade finite element with six degrees of freedom in each node has been developed. It represents a discrete annular set of identical sections of impeller blades. For its developing a defining system of equations, which was obtained by transforming differential equations describing the torsionalflexural oscillations of the blades was employed. The transformation is performed based on the use of the properties of the proper motions spectra of structures with rotational symmetry. The stiffness and mass matrices of the wave blade element were obtained by the Galerkin method wth the defining system of equations and linear shape functions. These matrices are Hermitian and establish a linear relationship between the amplitudes of traveling waves of displacements and forces on the inner and outer boundaries of the blade element. The developed finite element allows determining dynamic characteristics of the GTE blade rings. 
Blinov A. O., Borisov A. V., Mukharlyamov R. G., Goncharova I. A., Borisova V. L. Variablelength link model with controllable stiffness and movable pole for aerospace exosuit. Trudy MAI, 2024, no 136 The article considers a model of a variablelength link containing a magnetorheological fluid for actively controlling its stiffness under the influence of a changing external magnetic field. The distinguishing feature of the proposed model, compared to those created previously, is the presence of a movable pole at the lower point of the link with a specified law of motion, for example, due to the movement of a link positioned below. Thus, the link model has seven degrees of freedom: three translational movements of the pole, three rotations around the pole, and variable link length when the upper part moves relative to the pole. In the proposed link construction, all elements are modeled as cylinders or disks of finite radius. Moments of inertia are defined for them relative to axes passing through the link's origin for the three coordinate axes. It is taken into account that the amount of magnetorheological fluid below and above the piston changes as it moves inside the cylinder, with changes in the link's length. This changes the moment of inertia of the link. This determines the novelty of the research. The dynamics of the link are described by Lagrange's equations, constituting a system of seven ordinary secondorder differential equations. A softwarebased motion control method is selected, and based on it, the inverse dynamics problem is solved  determining the control moments and forces that need to be applied to realize the specified link movements. The created link model, when combined into a multilink structure, can find application in the development of exoskeletons in the form of spacesuits, protective exoskeletons enhancing and supporting the physical capabilities of pilots and astronauts in the aerospace industry. 
Kosenko I. I., Kuleshov A. S., Shishkov A. A. The Problem of Rolling a Ball on a Surface of Revolution and its Numerical Investigationю. Trudy MAI, 2024, no 136 When creating models of various technical devices and processes, mechanical systems with nonholonomic constraints are often used. As an example, the classical work of M.V. Keldysh [1] is worth mentioning, in which the nonholonomic mechanical model that described the shimmy effect, i.e. the phenomenon of intense angular selfoscillations of the aircraft front wheels [2] was proposed. That is why further studies of the classical problems of nonholonomic mechanics, which now can be studied with the stateoftheart mathematical, symbolic and numerical methods, present interest.
One of these classical problems of nonholonomic dynamics is the problem of a heavy homogeneous ball rolling without sliding along the perfectly rough surface of revolution. This problem has been considered at the end of the 19th  beginning of the 20th century in the works of E. J. Routh and F. Noether [3, 4]. Moreover, in these works, the surface on which the geometric center of the ball is located during movement, rather than the supporting surface along which the ball is rolling, was considered given. The article demonstrates how the ball motion equations can be reduced to the system of equations written in Cauchy form, i.e. reduce the problem of the ball motion to the Cauchy problem solving by defining the surface, along which the ball is moving, in an explicit form. Coefficients of the corresponding equations will depend on characteristics of the surface, along which the center of the ball moves, its principal curvatures and the Lame coefficients. If the equations of motion of a certain mechanical system are written in Cauchy form, then it is convenient to perform numerical analysis of the system under study. Thus, numerical analysis of the equations of motion of a rolling ball along the surface of revolution was performed by the MAPLE mathematical software. The numerically obtained results confirm the analytically proven statements about the ball motion. 
Krupenin A. M. New method for construction kinetic diagram by fatigue crack growth rate tests. Trudy MAI, 2024, no 136 The article proposes a new method for kinetic diagram plotting of the fatigue crack growth rate by experimental data.
The article is divided into nine parts.
The first part discusses the work relevance, as well as adduces links to the previously conducted research on this issue.
The second part provides general description of processing results of the experiments on fatigue crack growth rate.
The third part discusses specifics and limitations of the current method of results processing of the experiments on fatigue crack growth rate.
The fourth part gives and substantiates assumptions on the qualitative characteristics of experimental data.
The fifth part describes the proposed method for the results processing of the experiments on fatigue crack growth rate. Special basic functions with which processing is performed, are being introduced.
The sixth part performs the studies of the derivatives and integrals of basic functions.
The seventh part describes the methods for determining characteristics of the kinetic diagram. These are the boundaries of the second section, coefficients of the Paris equation and coefficients of the equation approximating the first section of the kinetic diagram.
The eighth part demonstrates the results of the kinetic diagram characteristics computing, as well as provides an example of the operating time computing for a compact sample.
The ninth part presents inferences on the work being accomplished.
1. The causes limiting accuracy of the classical methods for plotting a kinetic diagram are shown. The article demonstrates that the relative error in determining the FCGR through the ratio of finite differences is rather significant and it is not constant in the value of the argument of the V(N) function. Thus, computing the FCGR through the finite differences may lead to a significant error in defining the kinetic diagram and its characteristics.
2. The author introduces and substantiates the assumptions on the qualitative mathematical properties of experimental curves and kinetic diagram. The following properties such as monotony, convexity and the presence of an asymptote are being supposed for the experimental dependence l(N). For dependencies V(N) and V(ΔK(l)), we assume the following properties: smoothness, monotony, and the presence of an asymptote (for V(N)).
3. A new method for plotting a kinetic diagram of the FCGR from the SIF range based on the results of an experiment at the FCGR, with account for the qualitative characteristics of the experimental data has been developed. The said method allows obtaining a kinetic diagram not in the form of a scatter of points, but in the form of a smooth function, which, in its turn, allows considering the kinetic diagram characteristics, as well as some specifics of its behavior, including the first section of the diagram, in more detail.
4. Basic functions, by which experimental data is processed on the FCGR in the proposed method are introduced and studied.
5. Methods for obtaining the kinetic diagram characteristics, describing both the stage of steady growth and the first section of the kinetic diagram, have been developed.
6. The article demonstrates that the first stage of the crack growth may occupy a large part of the cyclic durability. 7. It was demonstrated that a less conservative solution than the solution obtained using only the Paris equation is being obtained with account for the first section of the kinetic diagram when computing the operating time. 
Snazin A. A., Sevchenko V. I. Numerical modeling of interaction blown argon jets system with supersonic flow. Trudy MAI, 2024, no 136 The search for optimal methods of interaction with supersonic flows using blown gas jets is an important and relevant area that is currently receiving great attention. In this paper, a detailed study of the mutual influence of a blown argon jets system with an incoming supersonic flow in the computational domain with and without a ledge is carried out. The angle of convergence and divergence of the blown argon jets was varied in order to study its effect on the efficiency of mixing argon with supersonic flow in the computational domain.
In this paper, a detailed study of the mutual influence of a system of blown argon jets with an incoming supersonic flow in the computational domain with and without a ledge is carried out. The angle of convergence and divergence of the blown argon jets was varied in order to study its effect on the efficiency of mixing argon with a supersonic flow.
When the angle is reduced to α = +30°, the argon distribution profile over the volume of the calculated area takes a cylindrical shape and shifts closer to its geometric center, which negatively affects the efficiency of mixing argon with supersonic flow. The addition of a ledge to the upper wall of the design area, which organizes the falling jump of the seal, leads to a restructuring of the shock wave structure. As a result, the crosssectional area occupied by argon at the exit from the calculated area increases, but the argon flow profile remains the same cylindrical. At a convergence angle of α =  30°, the area of the passage section at the exit from the design area becomes equal to 35%. When the blown jets diverge (α =  5 ° 30), argon is pressed more strongly to the bottom of the calculated area, especially when blown from the side holes. Further downstream, the argon blown out of the side holes expands, moves away from the plane of symmetry and twists as a result of the formation of a pair of large counterrotating vortices. Further, the argon flow profile expands more and occupies a larger crosssectional area of the calculated area. Adding a ledge to the upper wall of the design area at the maximum angle of divergence a = 30°. It allows to stabilize the crosssectional area occupied by argon in such a way that it does not change throughout the entire distance to the exit from the calculated area and is equal to d33%, which shows the best efficiency of mixing argon with supersonic flow. 
Ivanov M. Y., Gorodnov A. O., Laptev I. V., Sidorenko N. Y., Malahov A. S., Resh G. F. Features of Mathematical Modeling and Validation of Computer Model of Physical Processes in the Porous Mesh Material of a Hydraulic Filter Element. Trudy MAI, 2024, no 136 The paper considers the features of creating physical and mathematical model of spatial motion of viscous incompressible nonthermally conductive liquid in  a hydraulic filter element. Porous mesh materials are artificial porous media formed by several (more than two) flat sheets of metal grids, the fibers of which are rigidly interconnected. The relevance of adequate computer modeling of the functioning of the filter element is due to the need to develop a digital twin of hydraulic system containing such devices. Currently, Russian and foreign industrial enterprises are developing and using virtual analogues of physical processes, products and systems for the socalled predictive modeling of the development of processes and behavior of products and systems. This makes it possible to predict the nature of the features of the course of phenomena of various natures or the functioning of systems long before the occurrence of possible emergency situations throughout their entire life cycle. Based on the LOGOS AeroHydro engineering analysis system, theoretical method for determining the coefficient of hydraulic resistance of representative element (quasiperiodic cell) of porous mesh material of arbitrary configuration is proposed, implemented and confirmed in practice by solving the problem of liquid flowing around twolayer structure of the material. A computer model of virtual pouring tests of sample of porous mesh material has been developed, providing a relative error in determining the coefficient of hydraulic resistance of sample of porous mesh material of no more than 5%. The procedure for validating the computer model of nonstationary physical processes in the considered porous structure is described. Validation spill tests of porous mesh material sample confirmed the required level of adequacy and provided the required degree of accuracy of the computer model of the sample under study. The validation uses empirical data obtained from spillage tests of sample of porous mesh material. The simulation results supplement the fundamental theory of studying the hydraulic properties of porous permeable materials. The possibility of using the classical phenomenological DarcyForchheimer model of a porous mesh material sample in development of digital twins of pneumohydraulic systems has been confirmed. 
Basharina T. A., Levina A. V., Glebov S. E., Shmatov D. P., Drozdov I. G. Investigation of hydrodynamic processes in cooling systems of liquidpropellant rocket engines with additive porous structures. Trudy MAI, 2024, no 136 The development of rocket engine construction is characterized by an increase in the flight characteristics, service life, reliability and energy efficiency of liquid rocket engines (LPRE), which makes it urgent to improve and modernize the cooling systems of liquid rocket engines. In modern mechanical engineering there is no theoretical and experimental basis and proven analytical methods for calculating the characteristics of additive porous structures and the hydrodynamics of the working environment in the internal volume with full geometric identification of the inpore space. To increase the service life and energy characteristics of rocket engines, innovative design solutions and new production technologies are being introduced, the combination of which is reflected in the cooling system of a rocket engine with porous structures manufactured by additive manufacturing. A computational experiment and research hydrodynamic tests of the cooling tract of an engine with additive porous structures were carried out. In the course of research using the method of polynomial approximations, the criterion dependences of the viscous and inertial resistance coefficients of a porous structure manufactured by an additive method were determined. The applicability of the laws of the theory of filtration of porous bodies in additive porous structures with full geometric identification has been proven by setting up a mathematical model taking into account the superposition of viscous and inertial drag coefficients. The influence of the degree of anisotropy of the medium on the reliability of the computational experiment using a mathematical model taking into account the superposition of the viscous and inertial components has been established. 
Zakharov I. I., Aleroev T. S. About one method of approximate solution of the first boundary value problem for the fractional diffusion equation, used in gas dynamics. Trudy MAI, 2024, no 136 This paper is devoted to the development of fundamentally new analytical and approximate methods for studying mathematical models of advectiondiffusion using fractional calculus. Obtained results can have applications in various fields of applied mathematics and engineering. In particular, in the design of modern rocket engines (supersonic jet engines). The fractional operators for this problem are considered in the Caputo sense. The problem is solved by the method of separation of variables (Fourier method). In the first section of the paper the theoretical aspects of the problem are presented. An important part of this section is the construction of the basis of the systems of eigenfunctions and adjoint functions of the problem. In this question we strongly rely on the work of Dzhrbashyan and Nersesyan. Taking into account the biorthogonality of such systems and the fact that the adjoint functions are finite in number, for further solution we can consider only the problem in which the adjoint functions are not generated. Passing to the solution of the problem, we consider the system of eigenfunctions of the biorthogonal problem, since the basis of the eigenfunctions of the problem is not orthogonal in . In order to determine the unknown coefficients of the Fourier series, due to the biorthogonality of the systems of functions, we use the scalar product of the corresponding functions. The eigenvalues of the problem are found as zeros of the MittagLeffler function. Thus, to solve the problem, we first find several eigenvalues. We construct eigenfunctions and functions of the conjugate problem. Since for an approximate solution of the problem it is sufficient to take only the first few terms of the series, we can construct the solution surfaces by considering only the partial sum of the obtained solution. 
Dmitrievtsev A. Y., Zyryanov Y. T., Nuri A. N. . Trudy MAI, 2024, no 136 The article presents an algorithm developed by the authors, intended for the measuring system, constructed on the annular phased antenna array (APAA), diagnosing. The said array employs microstrip patches with exponential slot opening (Vivaldi emitter) as emitters, widely employed in radiotechnical systems, aviation and rocket engineering. The main advantage of the emitters applied in APAA is the wide range of frequencies, in which this emitter is able to operate without changing its geometric dimensions. A simplified method of the APAA directional pattern mathematical calculation of is considered. This approach allows performing calculations without reliability reduction of the soughtfor characteristics of the object being studied, but it does not consume herewith a large amount of computing resources of the equipment, on which computations are being performed, due to a decrease in the number of actions required for the computations. The main parameters diagnosing was being performed by highfrequency measuring equipment, which allows cconducting all necessary measurements, on which basis subsequent conclusions can be drawn. The results of the APAA measured parameters analysis were compared with the results of seminatural modeling, which confirmed the developed approach operability. The obtained measurement results differ to a small extent from the simulation results in a special software package. The main advantage consists in the ability of analyzing the main parameters of the APAA being diagnosed in real time, as well as the ability for comparing them with the simulation results performed in the software package. Due to this control method prospectivity, the authors plan further improvement of the method by automating characterization of the object being diagnosed. 
Orekhovich R. A. Methodology for functional reconfiguration of an onboard equipment complex of an unmanned aircraft vehicle. Trudy MAI, 2024, no 136 The article deals with the issue of ensuring the failsafe of the onboard equipment (OBE) complex of an unmanned aerial vehicle (UAV) with a long flight duration. This trend of research is a relevant aspect in the unmanned systems development. The UAVs find wide application in modern armed conflicts and various sectors of the economy. The number of tasks assigned to the unmanned systems increases annually.
Regardless of the scope of application and class of the UAV, the main property that the UAV must possess is its operational reliability. It is being ensured in various ways, such as redundancy, integration and reconfiguration, but the required values of reliability indicators are not being achieved. Creation of the redundant reconfigurable OBE is the only way to achieve maximum possible reliability of these complexes under conditions of both limited components in use reliability and the impact of a wide range of external factors. Modern approaches to the redundancy management are aimed at ensuring the functions performing of the failed components by the other OBE intact components.
The article describes an experimental technique for functional reconfiguration, which allows optimizing the OBE operation, ensuring its maximum efficiency and functionality. It is based on an adaptive method of the OBE functional reconfiguration, which consists in introducing of an adaptation block that generates functional efficiency indicators (FPE) of components, based on the application of the information about operating modes, operator commands and other external information, as well as information about the technical condition of functional modules based on the fuzzy logic approach.
To test the proposed methodology, a functional the OBE mathematical model was developed, which was realized in the MATLAB interactive environment for programming and numerical calculations with special tools for analysis, design and fuzzy logic systems modeling  Fuzzy Logic Toolbox. Operation of the said technique is considered on the example of the one of the OBE computer failure, of which results in the redistribution of tasks between the computers, which increases the probability of the combat mission completion. The methodology and mathematical model of the adaptive functional reconfiguration of the UAV OBE proposed in the article allows defining the PFE configurations of the OBE components based on a fuzzy logic approach, which in its turn allows completing a combat mission without losing the computational load with the available resources of the UAV OBE components. 
Osipov N. A., Musienko A. S. Increasing the validity of selective control of the onboard system during the operation of space assets. Trudy MAI, 2024, no 136 The article describes a technique that combines a priori (additional) information and current monitoring data from testing space assets to achieve the goal of selecting and achieving a better assessment of the object.
The proposed method is based on the mathematical apparatus of dynamic Bayesian networks, as well as the basic concepts and connections of reliability theory and technical diagnostics of systems. The initial data is information about the spacecraft elements technical condition during test monitoring, information about reliability (structural and logical diagrams, component failure rates) of technological equipment, as well as linked models for diagnosing various types of technical condition and signs of diagnosing component faults.
The article proposed to use the selection method in a dynamic Bayesian network to identify inconsistencies between products and devices in the process of monitoring and technical condition diagnosing of the technological equipment components and describing the its process dynamics.
A posteriori inference allows combining heterogeneous initial information and newly received data to obtain a comprehensive assessment of the technological process and the state of the technological device, so that the expert may make an better decision on whether continuing or suspending the technological process, if errors are detected, and take measures to eliminate them.
The advantage of this technique is its ability to account for a priori heterogeneous information, especially the format of the subjects under test representation and the results of control experiments.
The article presents this method implementation for controlled studies on a limited sample collection. This capability is being demonstrated based on the results of random inspection tests, which estimate the expected cost of a defective product in the entire lot with sufficient objectivity to make random inspection decisions.
The method under consideration combines a priori information and data obtained from test results, which, when compared, allows achieving the necessary accuracy in identifying product defects.
The proposed method may be employed by the specialists when conducting system monitoring and testing activities to increase the efficiency of selection and defective products identification. 
Novikov A. N. The method for the rational formation of weighting coefficients in the processing channels of a broadband adaptive antenna array. Trudy MAI, 2024, no 136 Fighter aviation plays an important role in ensuring security and sovereignty of the Russian Federation. Modern Russian fighter aircraft are equipped with the onboard radiotechnical complexes, on which the success of the assigned missions accomplishing largely depends. One of the main elements of any radio engineering complex is antenna, to which a number of requirements for primary signal processing is placed. Adaptive antenna arrys relate to the antennas allowing signal processing performing. The theory of adaptive antenna arrays has currently developed only for the narrowband, and more precisely for the harmonic signals. However, modern realities dictate the need to employ signals with a wider spectrum, which makes the theory of adaptive antenna arrays ineffective for such signals. Nevertheless, the developed theory of harmonic signal processing became the basis for the development of the theory of broadband signal processing in adaptive antenna arrays. The frequency representation of the signal, but not the time representation, is taken herewith as a basis. Analytical relations to form optimal weighting coefficients in the frequencydependent processing channels of the adaptive antenna array were revealed. Implementation of the optimal weighting coefficients is impossible in practice due to the continuity and infinity of the broadband signal spectrum. However, the optimal representation allowed formulating an approach to finding quasioptimal weighting coefficients, which essence consists in finding the optimal vector of weighting coefficients at certain frequencies of the spectrum of a useful broadband signal and its interpolation at other frequencies of the spectrum of a useful broadband signal by various interpolation polynomials. The frequencies herwith, at which the vector of weighting coefficients was optimally determined, were selected arbitrarily with the same discrete interval without accounting for the spectral structure of the useful broadband signal. However, the analysis demonstrated that at the frequencies, at which the spectral density of the useful signal is low, the interference signal is most effective and vice versa. In this regard, a method that accountы ащк the spectral density of the useful signal when forming quasioptimal weighting coefficients has been developed. This method allows to distributing rationally optimal weighting coefficients over the spectrum of a useful broadband signal and adapting to the interference signals more efficiently. 
Buzhin I. G., Antonova V. M., Pozdnyakov R. ., Mironov Y. B. Features of network traffic processing on thirdlevel switches with open operating systems. Trudy MAI, 2024, no 136 In modern control and information processing systems of aerospace aircraft, the use of whitebox switches with open network operating systems based on ASIC network chips as a network infrastructure is gaining popularity, thanks to which various network functions become available, independence from network equipment manufacturers appears. At the same time, the functioning of such devices and the principle of processing network traffic have their own characteristics that should be taken into account when operating white АВТОРЕbox switches. The purpose of the study: to identify the features of network traffic processing in whitebox switches and to develop some recommendations for their elimination. As a result, this article analyzes the hardware and software architecture of network equipment, as a result of which it is revealed that the architecture of a network device consists of a data transmission layer (Data plane) and a control plane. The Data plane layer is represented by an ASIC network chip with SDK and SAI tools. The Control plane level is represented by a CPU chip with a Kernel Routing (Linux) tool and a CLI. Also, as a result of the operation of whitebox switches, such traffic processing features as the desynchronization of Kernel Routing and ASIC, a violation of interface configuration logic and a decrease in port throughput were revealed. To eliminate these shortcomings, some recommendations have been developed, according to which, in order to successfully process traffic in whitebox switches, it is necessary to control the interface configuration on ASIC ingress pipelines, check the synchronization of Kernel routing Linux and ASIC. To maintain the required packet throughput, it is necessary to monitor the correctness of specifying egress interfaces and nexthop when processing traffic from input ports. 
Gavrilov K. Y., Kozlov R. Y. Construction of trajectories of movement of people during radar sensing of premises through a wall. Trudy MAI, 2024, no 136
The premises probing radars are mainly applied for detecting people, determining their number, location and trajectory of movement indoors. As in conventional radar, human detection procedures are based on threshold signal processing methods and reduced to the primary target markers forming. Here, however, the specifics of the operation of wallsensing radars are manifested, associated with the presence of strong interference noises indoors (due to the signals rereflections from walls, floor, ceiling, furniture) and leading to origination of a large number of false targets and abnormal values of the measured coordinates of targets. 
Tsymbal M. ., Semichastnov A. ., Balakin D. A., Udalov N. . Development of a digital twin of a groundbased radio navigation system based on the principles of modeloriented design using the mathematical modeling environment Engee. Trudy MAI, 2024, no 136
The article presents the main stages of the development of a digital twin for a groundbased radio navigation system. A modeloriented design approach is chosen as the methodology for development. The mathematical modeling environment Engee is used as a tool to implement a groundbased radio navigation system. 
Aliyeva A. J., Agamaliev R. . Research of extreme work regime of semiactive system for homing of guided missiles. Trudy MAI, 2024, no 136 Such aircraft striking means as missiles, projectiles, aerial bombs can be effectively used only if they function together with their target guidance system. When building criteria for the effectiveness of guidance systems, the important role of these weapons on the battlefield should be taken into account, as well as the requirement of high reliability of their delivery to the target. High efficiency of guidance systems can be achieved by applying advanced mathematical models of the guidance system control circuit. The created mathematical models and missile guidance algorithms must be tested using all possible optimization procedures. Such requirements are relevant not only for external guided missile guidance systems, but also for projectile homing systems and unmanned aerial vehicles. The presented article is devoted to the analysis of extreme operating modes of a semiactive guidance system of an optically guided missile at a target. The case of a heatemitting target and the use of pyroelectric sensors is considered. Two modes of operation of the system are analyzed: (a) there is a restriction on the movement of the emitter towards the target, (b) there is a restriction on the movement of the missile launcher towards the target. In the first mode, the functional dependence of the distance of the emitter to the target on the independent variable is determined when the functional of the target reaches a minimum. In the second mode, the functional dependence of the distance of the rocket launcher to the target on the independent variable at which the target functional reaches a minimum is determined. The identified two modes are characterized as extremely undesirable, which should be avoided. 
Ezrokhi Y. A., Kalenskii S. M. Method of the compressor characteristic representation in aviation GTE mathematical model. Trudy MAI, 2024, no 136
The presented article analyzes the basic methods of the compressor characteristic representation in aviation GTE (gasturbine engine) mathematical model (ЕММ). It considered specifics of their realization in the approximated and tabular forms, and marked advantages and disadvantages of both methods 
Bebeshko A. ., Ivanov P. . Mathematical model of the flight of the objectcontrolled gliding parachute system taking into account the terrain. Trudy MAI, 2024, no 136
The task of navigation and guidance of the object – guided gliding parachute system to the target is one of the most important in the theory and practice of guided parachute systems. The problematic part of this task is navigation and guidance in automatic mode under conditions of complex terrain relief and difficult wind conditions in the guidance zone. The presented article provides an example of developing a method and constructing a mathematical model for targeting the object – controlled gliding parachute system at a target, with account for the terrain relief in automatic mode (in radio silence mode). A program for the system navigation and guidance to the target point for the onboard computer has been developed. 
Balakirev N. E., Fadeev M. ., Rodionov V. . Qualitative approach in extracting the information content of wave data. Trudy MAI, 2024. Trudy MAI, 2024, no 136
This article examines the use of a qualitative approach in the analysis of wave phenomena, the features of studying waves as a qualitative aspect, and the introduction of new approaches in the analysis and synthesis of waves. The authors note that most pattern recognition systems based on wave phenomena use classical mathematical methods for modeling and analyzing data, focusing on quantitative characteristics. However, this article raises the question of a qualitative assessment of the data obtained and their content, and also considers the possibility of using a qualitative approach in disclosing the information content of data flows of wave phenomena. The dissection of such content is the basis for speech recognition or integral, informational analysis of complex natural phenomena based on the consideration of wave signals. 
Huseynova R. ., Gumbatov D. A. Optimization of the conceptual development of unmanned aerial vehicles. Trudy MAI, 2024, no 136
The issues of flight reliability aerodynamic ensuring occupy special place while solving the problems on the UAV design. The basic factors affecting the UAV flight range, such as flight altitude, velocity, wind impact, propeller operating efficiency, are being considered in the MALE UAV robust design method. Accounting for these factors in the robust design method, which includes both optimization and probabilistic analysis performing is a substantial advantage of the robust approach compared to the conventional optimization without accounting for random factors. The purpose of the presented work consists in further improvement of the robust optimization process by extra optimization procedures introduction into it to account for some random factors impact on the quality target of the UAV operation. The article adduces the problems of the UAV robust design in terms of minimizing the normalized random component of the UAV real key figure at the given goal value of the same indicator with account for the random affecting factors (flight speed, flight altitude). The authors computed marginal optimal ratios of random component of the given goal value and derivatives of the basic figure by random factors at which the optimization goal function random component reaches its minimum. 
Gataulin A. ., Babchinetsky S. . Convert object coordinates from image pixels to world coordinates using Python and Unity. Trudy MAI, 2024, no 136
The article adduces description of development and implementation of an algorithm for transforming coordinates of objects captured in an image from the camera installed on an unmanned aerial vehicle, as well as the development of a simulation employing the Unity engine to test the written algorithm and verify the obtained world coordinates. 
Bakharev A. ., Mesyats A. . Lower accuracy estimation of uniform rational approximation in georeferencing problems. Trudy MAI, 2024, no 136
This paper discusses the problem of determining the limitations of rational function sensor model. Rational function model (RFM) is a generalized sensor model; it approximates the complex rigorous sensor model by utilizing a multitude of parameters (coefficients). 
Panteleev A. ., Karane M. S. Approximate synthesis of optimal control of trajectory pencils of continuous deterministic systems with incomplete feedback. Trudy MAI, 2024, no 136
The problem of finding an approximate optimal control for deterministic control systems with incomplete feedback on measured variables described by ordinary differential equations is considered. The initial conditions are given in the form of a set of initial states, so the problem of controlling a pencil of trajectories generated by this set and the control law used is considered. To describe the set of initial states, as well as the position of this pencil over time, smooth finite functions are used, the values of which characterize the density of traces of trajectories inside the pencil. 
Rumyantsev N. ., Solovyov S. ., Pavlov D. . Rumyantsev N.V., Solovyov S.V., Pavlov D.V. An intelligent system for monitoring, diagnosing and predicting the condition of onboard spacecraft systems. Trudy MAI, 2024, no 136
The reliability of spacecraft (SC) flight control depends on making optimal and operational decisions on issuing command actions to the SC. Practice shows that in some cases, only issuing immediate execution commands can prevent the development of emergency situations (ESS). The correctness of solutions to such problems is increased by using artificial intelligence methods as part of the ground control complex (GCS), the use of which is aimed at accelerating the processes of identifying anomalies, increasing the accuracy and completeness of recognition of GSNs in the operation of onboard spacecraft systems, and reducing the influence of the “human factor”. The article examines the state of control technologies currently used in flight control of modern spacecraft. The main shortcomings of the control process are formulated, which are increasing taking into account modern trends in the development of space programs. 
Kuleshov A. S., Lobanova E. V. Analysis of the Hess integrable case in the problem of motion of a ball on a smooth plane. Trudy MAI, 2024, no 135 The problem of motion of a heavy nonhomogeneous ball on a fixed smooth horizontal plane is considered. This problem is similar in many aspects to the classical problem of motion of a heavy rigid body with a fixed point. Both of these problems can be represented in the form of Hamiltonian system with two degrees of freedom. For integrability of both of these problems, only one additional first integral is needed. The equations of motion of both problems have the energy integral and the area integral. There are known integrable cases in the problem of motion of a ball, similar to the Euler – Poinsot, Lagrange and Hess integrable cases in the problem of motion of a heavy rigid body with a fixed point. In this paper, we study the integrable case of the problem of motion of the ball, similar to the Hess case. Equations of motion of the ball are written using the special coordinate system, originally introduced by P.V. Kharlamov to study various problems of rigid body dynamics. The study showed that the equations of motion of a nonhomogeneous ball on a smooth plane in the Hess case and the equations of motion of a heavy rigid body with a fixed point in the Hess case have similar properties. In particular, it is shown that, as in the classical problem of the motion of a body with a fixed point, a qualitative description of the motion of a ball on a smooth horizontal plane is reduced to the integration of the second – order linear differential equation, and at the zero level of the area integral the equations of motion of the ball can be integrated in quadratures. 
Eliseev A. V., Kuznetsov N. K., Mironov A. S. Energy characteristics in the evaluation of elastic and lever ties in the dyad of a mechanical oscillatory system. Trudy MAI, 2024, no 135
Vibrational effects are, on the one hand, of great significance in realizing the processes of the parts hardening, the granular mixtures unmixing, ores transportation, granule materials dosing executed by technological units in various industrial brunches. On the other hand, they should be accounted for while creating vibration protection systems of transport and technological machines of various purposes including vibration machines and equipment. 
Feoktistov S. I., Andrianov I. K., Htet L. . The effect of the Bauschinger effect and material hardening on the occurrence of secondary plastic deformations during autofreting of a thickwalled cylinder. Trudy MAI, 2024, no 135 The scientific research is devoted to the problem of calculating thickwalled axisymmetric cylindrical shells under conditions of hydraulic autofreting by internal pressure. The known analytical solutions to the problems of pipe autofreting in most cases do not take into account the conditions for the occurrence of secondary plastic strains during unloading. The purpose of this study was to evaluate the effect of the Bauschinger effect and material hardening, as well as the geometric parameters of the cylinder and the magnitude of the plasticity region in the wall of the cylindrical shell on the conditions of secondary plastic strains during unloading. The paper considers a model of the behavior of the material under alternating loading, taking into account the hypotheses and assumptions made in solving the problem. An equation is obtained that allows us to determine the conditions for the occurrence of secondary plastic strains depending on the listed factors. Within the framework of numerical calculations, it is concluded that the size of the plastic region in the cylinder wall has a significant effect on the occurrence of secondary plastic strains during autofreting. The results of numerical calculations for an ideal elastoplastic material are presented. According to the results of the study, with an increase in the hardening modulus and a decrease in the Bauschinger effect coefficient, the ratio of the outer radius of the cylinder to the inner one, at which secondary plastic deformations may occur during unloading during autofreting, can significantly decrease, and with a decrease in the overvoltage coefficient – increase. 
Kondratenko L. A., Mironova L. I. Modeling the dynamics of multiply connected nonlinear mechanical systems using a new numerical method. Trudy MAI, 2024, no 135
The article regards the initial stage of an aircraft landing, particularly the Yak42 aircraft, as a dynamic process of a multi connected nonlinear mechanical system. Despite the measures taken by pilots on dampening vertical speed and angular oscillations of the aircraft during landing under the impact of the external factors, such as wind, or factors determined by the design properties of the aircraft or its components, there is a possibility that the landing speed may be exceeded and unacceptable angular oscillations occur. Such deviations, arising at the initial stage of the process under consideration, affect significantly the subsequent aircraft movement along the airfield. 
Nakhatakyan F. G. Loading of a radial rolling bearing with bombed rollers. Trudy MAI, 2024, no 135 The presented article has studied the problem of radial bearing rollers barreling in detail. It is indicated that due to the edge effect, occurring in roller bearings in the ringroller contact, concentrations of contact stresses originate at the ends of the rollers, the value of the latter herewith may be several times higher than the Hertz ones, in which concentrations of stresses are not being accounted for. Owing to this phenomenon, the load capacity of the bearing is drastically reduced. It is noted that one of the effective methods to countereact this phenomenon in roller bearings is the rollers barreling, and in this case, the problem consists in determining the “barrel” radius.
To solve the problem analytically, the author employs his previously proposed method for the contact parameters determining during interaction of the two circular cylinders under conditions of a skew angle. For this method application, the end sections of the roller are replaced with discs of different diameters. Practically speaking we get a stepped roller. However, as the thickness of the roller tends to zero (or their number to infinity), the surface of the roller is smoothed.
Further, a system of equations, namely the compatibility of deformations, displacements and gaps, on the one hand, and equilibrium, on the other is being compiled.
The obtained system of equations was solved in this work analytically. The optimal radius of the roller “barrel” has been obtained, which ensures the absence of the contact stresses concentration at the ends of the roller, which indicates an increase in the load capacity of the roller bearing.
The results may be employed in the design of rollingcontact bearing with increased load capacity. 
Popova E. V. Modeling the evolution of solitary strain waves in two coaxial shells of incompressible material with combined nonlinearity, containing a viscous fluid between them and in the inner shell. Trudy MAI, 2024, no 135 The article deals with the hydroelasticity problem formulation for the two coaxial cylindrical shells of the KirchhoffLove type, containing a viscous incompressible fluid in the annular gap and in the inner shell. The material of the shells is considered as incompressible and of a nonlinear law of stressstrain relationship and strain intensity. The shell dynamics equations are obtained for the case when this law has a tough combined nonlinearity in the form of a function with a fractional exponent and a quadratic function. The viscous fluid dynamics are being considered in the framework of the hydrodynamic theory of lubrication, i.e., the fluid motion is assumed to be creeping. The asymptotic analysis of the formulated problem of hydroelasticity is performed applying the twoscale perturbation method. As the result, a system of two evolution equations for modeling the onlinear longitudinal strain waves propagation in shells is obtained. It demonstrated that in the case of incompressible shell material, the presence of viscous fluid in the inner shell does not affect the wave process. The equations of the system represent the Kortewegde VriesSchamel equations. The exact partial solution for the obtained system of evolution equations in the form of a solitary wave with an arbitrary wave number is found for the case when that wave propagates in each of the shells. The new difference scheme for the nonlinear system of two generalized Kortewegde VriesSchamel equations based on the application of the Gröbner basis technique is derived for numerical simulations. Computational experiments have been perforomed to study the evolution of solitary longitudinal strain waves excited in shells. Numerical modeling has revealed that solitary nonlinear strain waves in the shells are supersonic solitons, as well as the presence of the energy transfer from one shell to another due to the fluid viscosity between them. 
Borshevetskiy S. A. Method for determining the location of additional supports of a simply supported Kirchhoff plate under random action. Trudy MAI, 2024, no 135 An integral trend in modern mechanical engineering is to increase the efficiency of manufactured products. In aircraft such as airplanes, this could be achieve by reducing the weight of the structure, which is achieved through the using of skins and panels, which are thin shells that are not capable of independently carrying any small load. Therefore, to increase rigidity, they are additionally fixed. The analytical approach to problems with large plates or shells with a large number of additional supports has many difficulties due to the size of the resulting system.
The main objective of the new proposed method is to obtain analytical relationships between the type of external load and the location of additional supports based on the conditions of structural rigidity. The problem solving in several stages and uses wellknown mathematical methods.
The first step is to determine the maximum size of a single segment of the structure that satisfies the required stiffness condition. For universality, the problem is solved using the influence function (Green's) and the system's response to a unit load is obtained in the form of the Dirac delta function.
The second stage is to determine the location of only four (and in a nonstationary setting, only two) additional supports. The solution is the maximum value of the radius of the location of the fastenings that satisfy the condition of structural rigidity.
At the third stage, the required number and location coordinates of additional supports calculating for the entire structure as a whole, with possible adjustments to the sizes of the resulting segments.
The last stage can be numerical verification using modern modeling and calculation methods.
The undoubted advantage of the proposed method is its analytical form of solving the problem, which allows the method to using for various geometric and physical characteristics of the plates, as well as to apply an arbitrary load to any place. In general, the technique could be extend to curved shells. This will require the transition of the equation of motion of the structure to the local coordinate system of the shell, which will subsequently allow the shell to be “unfolded” into a rectangular plate. At the same time, the analytical form of solving the problem, as well as the essence of the technique and its advantages, are completely preserved. 
Glazjuk Y. V., Demidov A. S., Kashelkin V. V. Study of bending of triangular crosssection carbon fiber beams. Trudy MAI, 2024, no 135 The spaceships, which are expected to fly over the next decades, include large structural assemblies. The largest of them is a refrigeratorradiator, which length may exceed one hundred meters. Its loadbearing base should be a frame made of beams of various crosssections: round, boxshaped and triangular. At present, carbonbased structural materials are considered the most suitable for the beams manufacturing. They demonstrate high mechanical, acceptable technological properties and they are of low density as well. The carbonbased materials specificity is that they exhibit various properties under tension and compression. Such materials are commonly referred to as multimodular. Obviously, the difference in modularity manifests itself while bending as well. The article considers the stress state of bent solid and thinwalled beams of triangular crosssection. It leads to certain difficulties at stress computing, since the neutral section line position while bending depends on the ratio of Young modules under tension and compression. The problem under consideration is being solved in the article by the analytical method. The crosssection of the bent beam is being divided into two zones by a neutral line. Tension stresses are acting in one of the zones, while compression stresses are acting in the other one. An equilibrium equation is drawn up and formulas for the operating stresses computing are derived. Structurally, the article is divided into five parts and consists of an introduction, analysis of stresses in a bent beam of solid triangular section, the same analysis of a beam of thinwalled triangular section, examples of computing and conclusions. When analyzing the stress state, the K function is used, depending on the ratio of Young's modules for tension and compression, on the shape and size of the beam section, as well as on the neutral line position. The article presents formulas for determining maximum stresses in the cross sections. It includes five figures depicting the view of the refrigeratorradiator section, cross sections of solid and thinwalled beams, graphs of K functions for such beams. The examples include comparative results obtained with and without account for the actual position of the neutral line in the beam section. Conclusions present recommendations on the requirement to account for the difference in modularity of carbonbased materials, which may be useful in engineering practice. 
Borisova V. ., Silantiev V. . Features of minimizing the induced drag of lifting systems with winglet. Trudy MAI, 2024, no 135
The presented article considers specifics of the aircraft lifting systems with winglets optimizing with a restriction on the geometry deformation of the base wing. The presented numerical approach to aerodynamic design allows increasing the aircraft aerodynamic lifttodrag ratio by reducing the lifting system drag in the cruising flight mode. The drag minimization problem is focused in this article on the induced drag reducing, which is stipulated by the shroud of free vortices. The wellknown Munk's stagger theorem application allows correctly compute optimal distribution of the circulation intensity in the Treftz plane and, as a consequence, find the minimum induced drag. The numerical approach to optimization is based on the idea of the aircraft lifting system replacing with a system of the discrete Ushaped vortices. According to the Munk's theorem, lifting vortex systems can be translocateed along the freestream velocity into one vertical plane with the the air load retaining (velocity circulation) along the wingspan, which ensures an optimal solution along the lifting system. However, in the case of employing this approach for a longrange aircraft, with mainly swept wings and high subsonic cruising speeds, there is an intensive increase in the air load in the end wing sections, which increases even more, when induced drag is minimized over the entire lifting system (full optimization). This leads to the earlier compressibility stall development or the aerodynamic shock stall. In such cases, optimization of only a part of the lifting system (partial optimization) is possible, where the basic wing geometry is fixed, and the induced drag minimization is being performed on account of special wingtips or the winglets installing. In the case of the partial optimization, a fundamentally new approach, formulated in the form of a new numerical method, which accounts for the mutual interference of the wing and the winglet, both separately and on each other is employed. At the initial stage, the known initial geometry of the base wing is used and the initial geometry of the winglet is specified. Then, using a direct computational program (AEROJET program, based on the Morino’s panel method), the initial air load distribution along the wingspan and the winglet span is being determined for a given lift coefficient. This condition of retaining the air load distribution nature along the base wing span serves in a first approximation as a condition for the invariance of its geometry. The load distribution along the winglet span (wingtip) is being optimized and its geometry is being determined based on the obtained data by the proposed numerical method using the direct computational program (AEROJET). Since in view of the changes in the winglet geometry, the air load distribution along the base wing does not correspond to its geometry, the iterations continue until convergence is reached. With the new numerical approach application, optimization and aerodynamic design of the model of the advanced technology demonstrator aircraft, developed at the Siberian Aeronautical Research Institute named after S.A. Chaplygin, were performed. The aerodynamic lifttodrag ratio increase was obtained due to the optimized winglets installation and was about 8.8%. To assess the of viscosity effect on the wake vortex computing, comparison of the results obtained by the AEROJET program (nonviscous fluid) with the results of computations by the OPENFORM program, based on the averaged NavierStokes equations (viscous fluid) were performed. The study of the wing model in the framework of the viscous fluid was performed with two turbulence models namely Spalart Allmaras and k–ω SST. The ordered computational grid with the corresponding block structure has a total number of elements  10 million cells, the number of cells on the profile is 342 pieces. When analyzing the results, a good agreement between the computations for both turbulence models and with the results obtained by the new numerical approach with the correct adjustment for flow viscosity when making estimates is marked. 
Temnov A. N., Shkapov P. M., Yan Naing O. . Free oscillations of a cryogenic rotating fluid in a cylindrical cavity. Trudy MAI, 2024, no 135 This paper deals with the free oscillations of a rotating ideal cryogenic liquid inside a cylindrical tank with rigid walls. Cryogenic liquids are characterized by nonuniform temperature and density changes during operation and storage. The most significant stratification of the cryogenic component occurs in the direction of the external mass force field. To investigate the motion of this mechanical system, it is reasonable to use a stratified incompressible fluid model. The proposed work is devoted to the study of free oscillations of stratified fluid in a cylindrical tank, fully or partially filled with fluid rotating with small and large angular velocities. Calculations of eigenvalues of free oscillations of a rotating cryogenic liquid at a given buoyancy frequency for internal and surface waves in the form of graphs are given. In science, nature and various technical applications, rotating fluids occupy an important place. They are widely used in engineering, for example, in centrifuges, hollow shafts of liquidcooled turbines and in stabilizing the rotation of rockets. Currently, there is a growing interest in the study of vibrations of cryogenic fluids filling finitesized vessels used in various applications. The obtained results show that different types of waves can be observed in a rotating stratified fluid at both low and high rotational velocities, depending on the magnitude of the numbers . The natural frequencies of these waves depend on the ratio of buoyancy forces and Coriolis inertia forces. The presence of stratification leads to an increase in the frequencies of free oscillations of the fluid for internal and surface waves. The study of oscillations of a rotating stratified fluid has shown that the spectrum of oscillation eigenvalues consists of two sets of real numbers: a twoindex set for surface waves (at low rotational velocity) and (at high rotational velocity), and a threeindex set for internal waves. 
Patrakov S. S. The method for assessing the stability of radio control of dynamic object in a complex interference environment. Trudy MAI, 2024, no 135 The article considers the process of information radio exchange in the aviation complex under conditions of a complex interference situation, when the input of the receiving unit receives not only a legitimate signal but the signals with the parameters adequate to those of a legitimate signal except the parameters carrying valuable information. The purpose of the research, which results are presents in the article, consists in the noise immunity increasing of the data transmission radio system of aviation complexes in a complex interference environment. Selection of the Doppler frequency of the signal as an additional sign of interference is substantiated. The interference detection probability was selected as the noise immunity indicator. The interference detecting condition is defined. The author developed a model of informational exchange in complexes under interference conditions with account for the Doppler shift of the carrier frequency The model is complex and includes an analytical model, on which basis the simulation model was developed. The presented simulation results indicate the possibility for interference detecting with varying degrees of accuracy based on the statistical approach. To implement the proposed approach, the algorithm for the interference impact detecting on the dynamic object is developed, based on tracking the Doppler frequency of the received signal at all points of the flight path. The existing methods of noncryptographic protection of information transmitted throug the radio channel of modern aviation complex from interference ensure a probability of interference detecting not greater than 0,75. To increase the interference detecting probability, the author proposed to evaluate the information exchange stability based on tracking the Doppler frequency of the signal and interference, of which implementation allows achieving a noise immunity index of a least 0,99. 
Malyshev V. ., Mitrofanov D. V. Logicomathematical description of the problemsolving process when designing the control system of an unmanned aerial vehicle. Trudy MAI, 2024, no 135 Trends in the development of artificial intelligence technologies, their introduction into complex technical systems such as robotic complexes, unmanned aerial vehicles, minimizing the human role in the process of analyzing information and developing control solutions allow us to develop promising intelligent technical systems capable of fully simulating human intellectual activity associated with solving problematic situations (tasks) that arise during operation. This circumstance requires the definition of the main stages and cognitive processes associated with human intellectual activity. The article discusses the main stages of solving the problem (task). Their mathematical description has been completed. A graphical interpretation of the process of achieving a goal in the process of solving a problem (task) is demonstrated. The cognitive operations performed during the solution of the problem (task) are highlighted. Each operation is described from the point of view of mathematical logic and set theory. A scheme for solving the problem (problem) is proposed. 
Meleshin Y. M. Research and development of xband antenna for wave formation with nonzero orbital angular momentum. Trudy MAI, 2024, no 135 The article presents the process of electrodynamic modeling, designing and testing of the broadband Xband frequencies antennas, forming the waves with both spherical phase front and waves with nonzero orbital angular momentum (OAM). Antennas manufactured by printed technology based on an equidistant antenna array of 16 elements and operating in the frequency range from 9 to 10 GHz have were under study. The article demonstrates the process of the required phase shifts computing at the antenna elements, as well as aerodynamic modeling of the signal separation and phase shaping circuitry. Antennas with spherical phase front, with spiral phase front for clockwise and counterclockwise spiral rotations (corresponding to the OAM modes +1 and –1) were designed and fabricated. Experimental studies of the antenna patterns in the far zone (at a distance of 8 meters) and in the near zone (in the range from 0.1 to 2 meters) have been performed. Studies in the far zone revealed that the pattern was of a difference shape, and the wave intensity in the direction normal to the aperture plane is 30 dB less than that of a similar antenna with a spherical phase front. The difference in the transmission coefficient herewith between the case with the identic modes and different pitches is less than 4 dB for the comparison sector from –30 to +30 degrees, which indicates that the mode purity is insufficient for these antennas at a distance of 8 meters. The studies conducted in the near zone demonstrate the possibility of signal separation at one frequency and one type of polarization through the application of the developed antennas with different OAM modes with a coefficient of mutual locking up to 14 dB. However, with the distance increasing up to 1 meter, this coefficient falls to 34 dB, which already indicates a significant degradation of the modes purity at this distance. Conclusions on the relevance of the issues concerning quality improving of the modes formed by the OAM and reducing the divergence of such waves were made by the results of this work. 
Ermilov A. ., Balashov A. ., Gyulmagomedov N. . Manufacturing of functional prototype of antenna array for the missile and space equipment using additive technologies. Trudy MAI, 2024, no 135 The article discusses the development and manufacture of an operating prototype of an eightelement antenna array, which operates in the L1 frequency range of satellite radio navigation systems, using additive technologies. The widespread use of an antenna array for receiving navigation signals is currently found in adaptive noise protection systems with digital generation of a radiation pattern of the required shape. Calculations of the radio technical characteristics of an elementary emitter of antenna array providing operability in the L1 frequency range of satellite radio navigation systems have been carried out. The emitter is made in the form of a ceramic microstrip antenna, which consists of a silver emitting element, a ceramic substrate, an exciting pin and a metal ground. The profile of the radiating element is made in the form of a square element with chamfers at the edges, so that the antenna element has a circular polarization of the electromagnetic field. The design of the antenna array consisting of a base and 8 radiators is described. The configuration of the developed antenna array was chosen taking into account the provision of minimum geometric dimensions and minimizing interference between the emitters. The maximum number of radio interference that can be suppressed by the antenna array is one less than the number of array emitters and is 7. To confirm the operability of the selected antenna array configuration, a working prototype consisting of microstrip ceramic radiators and a base was made. The base is a cutout from the side surface of a cylinder with a diameter of ~ 400 mm. The base is made of PLA plastic using 3D printing technology. To form a metal ground on the surface of the base, metallization with a thickness of 10 microns was carried out. The results of the VSWR measurements confirmed the operability of the antenna array in the L1 frequency range of the GLONASS and GPS satellite radio navigation systems. The results of calculations and measurements of the VSWR were compared. Analysis of the results of calculations and measurements of VSWR emitters confirmed the correctness of the selected geometric parameters of the antenna array. A slight difference in the characteristics of VSWR emitters is caused by the influence of the edges of the base located close to the emitter. The developed antenna array can be applied in noiseprotected receivers of navigation signals with adaptive formation of radiation pattern. 
Zvonarev V. ., Pitrin A. V., Popov A. S. Bit error probability computing at incorrect signal with binary relative phase manipulation reception in the presence of harmonic interference. Trudy MAI, 2024, no 135 To ensure the stability of information transmission by a radio channel, the effect of noise and interference is of great importance. In the systems with relative (differential) phase manipulation (OFM), the socalled “reverse operation” mode is excluded. These signals are not much inferior in noise immunity to the phasemanipulated (FM) signals. Besdies, incoherent reception (demodulation) is possible, which greatly simplifies the receiving device. Such signals application and incoherent reception is preferable in cases where the phase of the carrier oscillation changes dynamically and/or randomly, and its tracking is difficult, especially in the presence of structural interference of various types. Let us determine both radio signal and interference models to compute the bit errors probabilities. We derive formulas for computing the average probabilities of the bit errors of incoherent reception of a radio signal from OFM2 in the presence of the linearly frequencymanipulated interference. The graph of the bit error probability dependence on the signaltonoise ratio at fixed values of frequency deviation and interference levels shows at what level the signal is ensured with the required values of the probability of a bit error. The graph of the bit error probability dependence on the magnitude of the frequency deviation is symmetrical with respect to its zero value. The curve in each direction has a wavelike appearance with decreasing minimum and maximum extreme values. Analyzing the obtained graphs, it can be noted that for certain, welldefined values of frequency deviation, the influence of interference with the LFM is minimal, and the less this effect is, the lower the level of interference. On the other hand, for some values of frequency deviation, the interference effect in the bit error probability metric is 34 orders of magnitude higher than the minimum values. The presence of interference leads to a dependence of the error probability on the value of the initial phases of both the signal and the interference, even under conditions of incoherent reception. To obtain a phaseaveraged value of the bit error probability, statistical averaging over the initial phases is necessary.
The developed technique allows qualitatively or conditionally quantifying the effects of linearly frequencymanipulated interference on the reliability of transmitted information in the radio channel when the interference frequency is shifted. 
Mukhtarov E. ., Petrov A. . Analysis of distortions occurring during signal filtration with linear frequency modulation. Trudy MAI, 2024, no 135 When processing a signal with linear frequency modulation obtained from radar equipment, there is an issue of undesirable distortion when compressing the signal using quasiconsistent filtration. These distortions occur due to minor deviations in the parameters of the signal's frequency change, which lead to a noticeable expansion of the response function. Such expansion, in turn, reduces the spatial resolution capabilities of the radar. In addition to the factors mentioned above, it is worth noting that during the transmission of the signal through the path, nonlinear distortions occur, which affect the amplitudephase characteristics. These distortions, in turn, lead to a number of additional problems. One such problem is the appearance of multiple echo signals. As a result, false targets and noises may appear on the image, and image fragments may also be shifted. This article discusses issues related to the construction of a mathematical model and the development of algorithms for generating signals with linear frequency modulation. Special attention is given to the quasiconsistent filtration of these signals, taking into account the influence of nonlinear distortions in the passthrough information path. The theoretical concepts presented in works [15] are used to create these models, and issues related to the generation and quasiconsistent filtering of signals, considering nonlinear distortions that may occur in the information pathway, are also considered. In conclusion, graphic material is provided that demonstrates the results of numerical analysis of distortions that occur during the processing of signals with linear frequency modulation. Such analysis allows for a more detailed study and understanding of the nature and scale of distortions, as well as determining possible methods for their elimination and minimization. At the same time, this material is an important tool for further research and development in the field of signal processing. 
Dudaev M. ., Pykhalov A. . The mathematical modeling of the dynamic behavior of twinrotor turbomachine systems with an intershaft bearing. Trudy MAI, 2024, no 135 The uptodate problem solution on enhancing cost effectiveness, applicability characteristics and other parameters of the gas turbine engines (GTE) of both aviation and ground purposes stipulated the multirotor (multistage) of the rotor system (RS) layout, which realization is most often associated with the interrotor (intershaft) bearings. The goal of the study presented in the article consists in further development of mathematical modeling and analysis of dynamic behavior of the GTE rotor system based on the double pass layout of its structure. The system consists of lowpressure and highpressure rotors, between which an intershaft bearing, serving as a support of the highpressure turbine rotor on the lowpressure rotor shaft, is placed. A mathematical model of the RS GTE dynamic behavior analyzing is based on the finite element method (FEM) and the theory of elasticity contact problem solution, which allows accounting for the coupling conditions of the parts in the rotor designs. The presented mathematical model is implemented in the form of a software package (solver). In the proposed mathematical model, the stiffness is represented as the sum of structural, contact and gyroscopic components and additional stiffness caused by action of centrifugal forces. The forced oscillations excitation model includes forces caused by static and dynamic imbalances of HP and LP rotors rotating with dissimilar operating frequencies, forces of parts contact interaction, and other forces. The Rayleigh mathematical model was used to simulate damping at the RS. Using the presented mathematical model, the amplitudetime characteristics (ATC) of a modern gas turbine engine rotor system are obtained, as well as a deformed state picture and the dynamic stresses field. A comparative analysis of the RS dynamic behavior results without accounting for the effect of the intershaft bearing and with one demonstrates in particular the additional harmonics appearance in the RS rotational frequencies operating range and the interference of vibrations in the form of an ATC blurring. 
Snazin A. A., Sevchenko V. I. Numerical simulation of interaction directional shock wave and transverse gas get blown into supersonic flow. Trudy MAI, 2024, no 135 Efficient interaction of blown gas jets with supersonic flow is one of the topical issues, to which a large number of researches and developments are devoted. Blowing jets into supersonic flow, is a common method of increasing the efficiency of gas mixing and influencing the shockwave structure of the flow. Studies show that transverse gas jet blowing is one of the traditional and reliable methods providing fast gas mixing and high penetration of the jet into the supersonic transverse flow [13]. The object of study is a channel with dimensions l = 180mm, h = 30mm and w = 80mm, where at a distance b = 80mm from the inlet there is a gas jet blowout point. At a distance n = b /2 there is a ramp of length m = 5mm and 10mm, and angle of inclination β = 30^{o}. The impinging supersonic flow is given by M_{∞} = 4.2, static pressure P_{∞} = 1200 Pa, and static temperature T_{∞} = 227 K. The Mach number of the blown jet is M_{j} = 1, the total temperature Tj = 293 K, and the ratio of jet pressure to static pressure P_{j}/P_{∞} = 0.16 [4]. The jet blowing condition was fixing throughout the calculation. The sticking and adiabatic wall condition are imposed on the lower and upper walls of the channel. The model was solved using the Reynoldsaveraged NavierStokes equations, which were closed by the SST kω turbulence model equation. [5] The mesh topology was constructed to resolve nearwall flows and turbulent structures in areas of large gradients of gasdynamic parameters. In nearwall regions, the dimensionless layer height y+ < 1. The total number of finite element mesh cells is 1.6×106 elements. Half of the channel was modeled and the symmetry condition was imposed on the interface plane. As a result of this research, a picture of shockwave structures was obtained and a numerical study of the interaction between a falling compaction jump and a transversely blown gas jet was carried out. The size of the ledge was varied in order to investigate its effect on the supersonic flow in the channel. As a result, it is obtained that increasing the size of the ledge has a great effect on the flow structure in the channel. In this case, the falling compaction jump formed in front of the blown gas jet is shifted closer to the channel entrance. Considering this tendency, it can be assumed that at a sufficiently large pj/p∞ ratio, the falling compaction jump can be displaced to the channel entrance, since the increase of the ledge leads to greater compression of the supersonic flow in the channel. Further increase in the size of the ledge can lead to "locking" of the channel, which in turn is an unfavorable condition for mixing of the blown jet gas and the surging flow. Also, the shockwave structure near the blown jet changes, the zones of wall layer detachment increase with increasing intensity of the compaction jump formed by the ledge. 
Genov A. ., Osipov V. ., Matsykin S. ., Savilkin S. S. Mathematical modeling of digital methods for the formation of the amplitudephase distribution of emitters in the xband. Trudy MAI, 2024, no 135 The use of multiservice onboard digital platforms and multibeam antennas as part of the spacecraft will make it possible to implement highspeed direct communication between subscriber earth stations in the Xband. In this article the results of mathematical modeling of digital methods for the generation of the emitters amplitudephase distribution (APD) in the Xband. The complex special feature is the digital processing of broadband information signals in the receiving and transmitting paths and digital methods for generating rays polar diagram (PD). The 16channel receiving and transmitting sublattices (RTS), each consisting of 16 receiving and transmitting modules (PTM) combined with a single control unit, were used for the insurance of the specified technical requirements of the communication complex. For the transmission path there are two separate beams with independent amplitudephase distributions of signals in the opening of each sublattice. For the receiving path there are also two separate beams with independent amplitudephase distributions in the opening of each sublattice, and the diagramforming circuits of the receiving beams in each module have common elements: lownoise amplifiers, mixers and intermediate frequency amplifiers, and the formation of beams for a given APD is carried out digitally after the ADC of the received signal on the second intermediate frequency. The generation of the signals’ amplitudephase distribution in the opening of the sublattice for each of the two beams is carried out independently in the FPGA digitally at a low frequency of 15 MHz received from the reference frequency block. For each beam in the FPGA, a group of 16 phase divider counters is used with individual control of the offset of the counting sequence in each counter, necessary for the formation of a predetermined amplitudephase distribution of ray signals in the opening of the sublattice. Digital phase control of the signals allows for strict phase binding to a single reference signal of the base frequency and eliminates the need for tuning elements that compensate for temperature instability, elements’ aging and other problems of analog and digital phase shifters. The mathematical model of the algorithm for generating a given APD of sublattice signals at a low frequency of 15 MHz in FPGAs was developed in the VHDL programming language. In the mathematical model structure, the diagramforming scheme of the transmission path, the generation block of a given amplitudephase distribution is represented by a developed user program. All other blocks of the mathematical model of the transmission path are designed without the user programs by directly using standard procedures and functions included in libraries. The simulation results verified the physical realizability of the receiving and transmitting sublattices in accordance with the specified functional schemes of the receiving and transmitting paths of the diagramforming scheme. 
Titov Y. ., Sudakov V. . Modification of the asynchronous ant colony method for searching for rational solutions to a parametric problem. Trudy MAI, 2024, no 135 The article considers the ant colony method modifications for application in the problems of searching for optimal values of system parameters. The parameters optimality is being determined by the values of the objective function computed as the result of complex computations of a mathematical or simulation model running on a separate computing cluster with the ability for parallel computing of the objective function values. To save the computing cluster resources, the already considered parameter values and the value of the objective function are stored in hash tables. Modifications of the ant colony method are being developed to solve the problem of stagnation, convergence to one rational solution, and allow the method to be applied to find the optimal solution without using the multistart procedure. This is achieved by modifying the behavior of the agent ant; the ants continue to search for a new set of parameter values that have not yet been considered on the cluster. Thus, each ant agent searches for its own unique route. As the result, the modification of the ant colony method does not converge to one solution, but continues to search for other solutions, avoiding stagnation and ensuring a complete directed search of all solutions (values of system parameters). This modification determines optimal and rational solutions in the early (estimate of mathematical expectation) iterations of the method. The authors proposed an asynchronous modification of the ant colony method for the effective work with a remote multithreaded computer. Each ant agent searches for its unique set of parameter values in a separate thread and, after finding it, sends a new task to the computing cluster via TCP sockets. The tasks received on the computer are buffered and sent to the dispatcher for uniform and constant loading of the computational threads. of The ant agents blocking associated with the addition and evaporation of pheromone is solved by the blockingfree RCU (read, copy, update) algorithm. A separate thread controls creation of a new graph with an updated pheromone, and all new agent ants will look for paths in the already new graph. 
Tarasov D. Y., Sukhomlino G. L., Mikhailov V. V. Numerical modeling of stepdown pulse dcdc voltage converters regulated by digital feedback. Trudy MAI, 2024, no 135 In the introductory part of the article, it is noted that in the research works of design organizations related to the development of regulated stepdown pulse DCDC voltage converters, approaches based on the use of such powerful software complexes as MATLAB/Simulink have been widely used. At the same time, the direction associated with the development of simpler computing tools remains in demand, which can be relied on not only when conducting specific computational studies of the designated converters, but also to confirm the reliability of the results obtained on the basis of these software packages. The purpose of the article is to describe two computational models designed to solve problems of dynamics of a stepdown pulse DCDC voltage converter controlled by digital (proportional, integral and differential) feedback. One of the models performing frequency analysis is designed to calculate the stability of the regulated converter in question. Another model based on the numerical integration method is focused on the study of transient and steadystate modes in the operation of the same converter. The main content of the article is devoted to the description of the designated two computational models. The calculation scheme of a stepdown pulse converter is presented here and the corresponding (based on an approximate "continuous" calculation model) dynamics problem is formulated in the form of a system of two firstorder differential equations (with respect to the current i in the throttle and the voltage U_{Н} of the load). It is indicated that an important requirement for this type of converter is its ability to reliably maintain the required value of the load voltage, which can be provided by including a feedback link in the circuit of operation of such a converter. It is assumed that the control system of the converter under discussion is based on the use of a digital PID controller in the feedback structure (which has the capabilities to implement proportional, integral and differential communication). A linear differential equation describing the functioning of the feedback link is written. Based on the obtained relations, a linear differential equation is formulated that establishes the relationship between the control parameter at the input and output of the open loop of the control system under consideration. An algorithm for calculating the frequency characteristics of such an open loop is presented. (Based on their analysis, a conclusion is made about the stability of the closedloop control system). A system of linear differential equations describing the dynamics of the controlled (feedback) stepdown converter is also formulated. An algorithm for the numerical solution of this type of dynamics problem based on the use of an implicit Euler scheme is presented. Examples of the application of the proposed two computational models to the study of the dynamics of a specific controlled stepdown converter are given. The final part of the article contains conclusions on the research performed. A brief description of the two proposed computational models is given here. It is also indicated that the reliability of the results obtained using these computational models is confirmed by practical coincidence with the results of computer modeling and physical experiment available in the literature. 
Minakov E. P., Aleksandrov M. ., Mishcheryakov A. ., Mishcheryakov S. . Algorithm for determining the parameters of oblinated projections of points on the earth's surface for circular orbits of space vehicles. Trudy MAI, 2024, no 135 The task of determining the parameters of inclined projections of points on the surface of the Earth and the algorithm for determining the parameters of inclined projections of visibility zones of point objects for circular orbits of spacecraft of remote sensing of the Earth are presented, as well as an example of determining the boundaries of the inclined projection of parameters of inclined projections of visibility zones of point objects for circular orbits of spacecraft of remote sensing of the Earth. An approach is being considered to assess the effectiveness of the use of Earth remote sensing spacecraft, based not on route calculations, with significant computational costs, but on the use of inclined projections, which significantly reduces these costs. The obtained results demonstrate a high degree of coincidence of the longitude of the projection boundaries of the visibility zones of Earth remote sensing spacecraft with points for routes and inclined projections for both straight and reverse orbits, which indicates the adequacy of the proposed algorithm for determining the parameters of inclined projections of the visibility zones of point objects for circular orbits of Earth remote sensing spacecraft. The algorithm allows you to obtain correct results, has extremely high information and operational characteristics and provides the opportunity to calculate inclined projections for groups of the same type of spacecraft of remote sensing of the Earth exactly once. This makes it possible to recommend a developed algorithm for solving the problems of determining coverage data and assessing the effectiveness of their application by regions on the Earth's surface for circular orbits of distan spacecraft 
Balashov E. V., Sentsov A. A. Simulation of the antenna directional pattern motion during conical scanning under conditions of angular carrier evolutions. Trudy MAI, 2024, no 135 The article deals with the description of a mathematical model of the directional pattern of the radar coordinator antenna in space, with account for fluctuations in pitch and yaw angles. The angular evolutions effect on the direction finding result is stipulated by the ratio of the angular velocity of rotation in the angle of roll and the angular velocity of evolutions. the presented article considers the case when these speeds are comparable. After considering a number of simplified models for analytical description of motion of the threedimensional antenna directional pattern in the “azimuth  angle of location” coordinates, a threedimensional model was computed, as well as its projection onto the Earth surface. The mathematical model correctness is confirmed by experimental studies, which results were obtained as an outcome of a radar coordinator installing on a linearly moving unmanned aerial vehicle, which is subjected to angular evolutions and implements the directionfinding method of conical scanning. Thus, the concept of a mathematical model of motion of the the directional pattern of the radar coordinator antenna projection onto the Earth surface, performing a conical scanning of space under conditions of linear displacement and angular evolutions of the carrier, is proposed. The said model is applicable for the devices and products functioning as a radar coordinator for various purposes. The model is based on a number of simplifications, such as linear motion models and the Gauss model for describing the antenna pattern. The adopted simplifications may be clarified without significant reworking of the model. 
Masliev A. ., Khismatov I. . The system of methods for analyzing, predicting and optimization of trajectory conditions of laser semiactive guidance systems. Trudy MAI, 2024, no 135 The study is devoted to improving the performance of flight tests of laser semiactive guidance systems (LPS) by predicting the ranges of the laser spot at the test site based on the results of the analysis of a statistical sample of previously conducted experiments. The analyzed statistical sample is formed by the method of mathematical modeling, the input information for which is the results of recording the detection range of the laser spot, the characteristics of the illumination and reception equipment, weather conditions and reflective properties of the target used. Based on the linearization of the relative mathematical expectation of the input information vector of the mathematical model, an expression is obtained for the variance of the error in calculating the threshold energy flux at the optical radiation receiver, depending on the variances of the information used. The relative weights of the errors of the input information in the structure of the error in calculating the threshold radiation flux were determined, an assessment of the consistency of the calculated values of its dispersion with experimental data was performed, the results of which confirmed the adequacy of the developed mathematical model in terms of reproducing the factors acting in the "sublighttargetreceiver" system. The prediction of the detection ranges of the laser spot is performed depending on the planned trajectory conditions, characterized by the transparency of the atmosphere on the tracks, the illumination angles and the sight of the target. An indicator of the reliability of forecasting is the probability of spot detection in a given range of ranges, which is estimated based on information about weather conditions, trajectory parameters and the obtained estimates of the variance of the results of threshold flow modeling. A mathematical model has been developed for the distribution of the radiation energy flux at the LPS receiver, depending on the characteristics of the trajectories of reception and illumination of polygon targets, weather conditions. The mathematical model differs from the known ones by using experimentally determined indicators of brightness coefficients distributed over the surface of the polygonal target model, which makes it possible to take into account its optical and geometric characteristics in calculations, which have a significant impact on the results of the LPS function. The results of mathematical modeling have been confirmed by field flight experiments. It has been established that the optimal conditions for conducting flight experiments according to the criterion of the minimum variance of the calculated threshold values are conditions in which the detection range is maximum. The use of the developed methodological apparatus in the planning of flight tests will reduce the degree of uncertainty, increase the reliability of the analysis results, as well as develop procedures for searching for optimal conditions for conducting flight experiments, eliminating discrepancies in the interpretation of their results. 
Aliyeva A. J. Issues of optimizing the application of the empirical linearization method for vicarious calibration of uav radiometric equipment. Trudy MAI, 2024, no 135 Currently, the empirical linearization method is widely applied to process images obtained from the UAVs, in particular to obtain data on reflection coefficients from optical radiation data. The gist of this method consists in placing calibration panels on special polygons and obtaining on this basis linear ratios between the DN (i.e. primary digital readings) and reflection coefficients, provided that data on the reflective characteristics of these panels are available. To ensure the best approximation of the linear dependence, a pair of such panels is employed: one is light, and the other is dark. The author regarded the possibility of applying a twopanel empirical linearization method in relation to a multispectrometer with a sufficiently large number of spectral channels. The gist of the twopoint (twopanel) method consists in converting digital samples into an indicator (coefficient) of reflection. This method realization involves the following operations: (1) Digital counts normalizing according to the following formula. (2) Converting the DC_{norm} of each pixel into the reflection coefficient of the object. The author proposed an adaptive mode of a multispectrometer operation, in which the exposure time of a fixed pixel on the spectral channel used depends on some technological indicator b_{i}/g_{i}, as well as determines the value of the DN_{raw}. A liquid crystal converter herewith is installed at the input of the multispectrometer, forming sequentially harmonics of the input signal with a controlled exposure time at the output. The process of sequential formation of narrowband reflection coefficients of the studied objects is optimized during calibration of a multispectrometer calibrated by the two (light and dark) calibration panels. An optimization problem has been solved in relation to a multispectrometer with sequential digitization and formation of spectral channels based on a liquid crystal converter, which essence consists in reaching the computed spectrumaveraged value of the reflection coefficient of the maximum value. 
Tran Q. T. Identification of the single ply properties in fibermetall lamintes. Trudy MAI, 2024, no 134 The paper presents the results of identifying the elastic characteristics and loss coefficients of monolayers of a metalpolymer composite consisting of layers of aluminum alloy and fiberglass (aluminum fiberglass). Identification was carried out on the basis of tests for damped vibrations of cantilevermounted samples. For dynamic testing, the samples were rigidly fixed with a metallic clamp at one end, leaving the other end free. Subsequently, an impact was applied to the free end using a metallic striker, or an initial deflection of the beam’s end from the equilibrium position was set. Displacements in the free end zone of the samples were measured by a laser displacement sensor and transferred to a program that allowed for the registration of displacement/time curves, saving them in tabular and graphical formats. The length of the free end of the beam, denoted as L (excluding the clamps), was determined to achieve a specified natural frequency of beam oscillations ω_{0} (20, 30 or 60 Hz). Specific values of lengths were used for beams with different laying schemes. The maximum deflection of the beam was A_{0} = 0.08L. The tests measured the natural vibration frequencies and loss coefficients of composite samples with various reinforcement schemes. Identification is performed based on solving the inverse problem using the classical theory of multilayer beams and the complex module method. Three approaches to solving the inverse problem are considered, in which a separate identification procedure is carried out for the elastic characteristics of monolayers based on the results of static or dynamic tests, or simultaneous identification of elastic and damping parameters is carried out based on dynamic test data. 
Shavelkin D. S. On the mechanisms of buckling of modified composites with viscous fibers. Trudy MAI, 2024, no 134 The presented work studies stability of modified composites with whiskerized fibers. The following problems are being solved within the framework of the study: the static problem of local loading and the problem of stability of layered cantilever rods made from the composites under study. When solving the static problem of local loading, a modified fiber composite, loaded by compressive forces along the fibers, which is accompanied by various fracturing mechanisms stipulated by the of the fibers bending, is being considered. It appeared that an interfacial layer with adjustable rigidity allowed, with the same volume fraction of reinforcing fibers (for a classical composite, the reinforcing element is fiber, and for the modified composite under consideration, a fiber with nanostructures grown on its surface) achieving significantly greater local stability, determining the characteristic type of microdamage at compression. When solving the problem of stability of the rods made from the composites under study, layered rods with different laying patterns and different volumetric contents of inclusions were considered. Critical load factors were determined for each of the studied samples. An analysis of the influence of the volume content of the modified fiber on the minimum critical values of compressive stresses showed that the stability of the modified composite can be increased by more than 2 times compared to the stability of a similar classical composite. When studying the stability of layered cantilever rods, it turned out that modification of the fiber with a mustache makes it possible to increase the value of the critical load withstood by the rod by more than 1.9 times compared to the critical load withstood by a rod made of a classic fiber composite with the same volumetric content of inclusions for any of the considered schemes laying of reinforcing fibers. 
Popov I. P. Mechanical energy accumulator with capacitor characteristics. Trudy MAI, 2024, no 134 Shortterm peak loads of machines and mechanisms create the need to accumulate mechanical energy for its subsequent pulsed use. This is quite relevant, for example, for airfield tractors at the initial stage of towing heavy aircraft. The use of a mechanical energy accumulator will reduce the power of the tractor engine. The mechanical energy accumulator can be made in the form of a direct current electric machine or a valve machine, on the shaft of which a superflywheel is attached. When a machine is connected to a power source, a nonstationary process occurs, described by two differential equations: one for mechanical quantities, the other for electrical quantities.
From the resulting formulas it follows that for an electrical circuit, the mechanical energy accumulator in question is indistinguishable from an electrical capacitor. It follows from this that in this case we can talk about artificial electrical capacitance. In addition, artificial electrical resistance arises (which is not related to the resistivity, length and crosssectional area of the conductors. In connection with the above, a mechanical energy accumulator can be interpreted as an artificial electric capacitor, which stores not the energy of the electric field, but the kinetic energy of rotation of the superflywheel. There are superflywheel designs that can store significant kinetic energy. Even the possibility of installing them on passenger vehicles was studied. In this sense, massive airfield tractors have an undeniable advantage, since the increase in weight is not only not problematic for them, but in some cases it is desirable. 
Sedel'nikov A. V., Serdakova V. V., Nikolaeva A. S. Checking the adequacy of approximate analytical dependences for the deflection of a thin homogeneous plate under temperature shock. Trudy MAI, 2024, no 134 The paper presents a comparative analysis of approximate analytical relationships modelling the deflection of a homogeneous thin plate under thermal shock for the case of rigid fixation of one edge of the plate and free other edges of the plate. This analysis contains two directions: studies of the deflection temperature field.
The temperature field of the plate is analysed by comparing the results of numerical simulations with the data of insitu tests. The experiments conducted with a new promising solar panel ROSA (RollOut Solar Array) in 2017 on board the International Space Station (ISS) were chosen as field tests. During these experiments, temperature measurements were made with sensors in different parts of ROSA, which allows a more correct comparison of modelling results with measured data. The comparison showed a good convergence of the results, especially near the fixed edge of ROSA. This is due to the closer real picture of the temperature shock to the mathematical formulation of the twodimensional heat conduction problem.
To confirm the obtained results, a comparative analysis was made with the data of experiments conducted in ground conditions of the space environment simulator laboratory KM7 with the space boom section. The results of numerical modelling and insitu experiment also have good convergence. And their differences are due to the fact that the beam model is more suitable for the boom than the plate model.
To investigate the fit of the deflection field, an experiment conducted with a reduced model ROSA solar panel in earth laboratory conditions was chosen. The deflection dynamics of the ROSA end section support beam was chosen as data for comparison. A good convergence of the results in the average value of deflections without taking into account thermal oscillations is shown. Since in the mathematical formulation of the thermoelasticity problem thermovibrations were not taken into account.
Thus, as a result of the work the limits of applicability of approximate analytical dependences for practical use in accounting for the temperature shock of solar panels of a small spacecraft have been revealed. The results of the work can be used in the study of rotational motion of a small spacecraft around its centre of mass taking into account the effect of temperature shock. 
Dobryshkin A. Y., Sysoev O. E., Sysoev E. O. Experimental verification of the characteristics of vibrations of a composite cylindrical thinwalled shell with a rib. Trudy MAI, 2024, no 134 The article performed an experimental verification of the oscillatory process characteristics obtained based on the mathematical model of oscillations of a thinwalled cylindrical shell by the improved Fourier series method. An analysis of the obtained data was conducted. A simple and at the same time accurate solution, based on the solution by the Fourier series method (FSM) applied in the analysis of the cylindrical shells vibrations is described. Hinged support is employed as fastening. The displacement function is expressed in each structural element in the form of superposition from the double Fourier series and several additional functions. The unknown deformation parameters are being found as generalized coordinates and determined by the RayleighRitz method. The use of The Fourier method application for the complex problem of a combined plate and shell connected by a symmetric and asymmetric boundary can be obtained without equations of motion or displacement expressions transforming.
The rigidity of fastening may significantly affect the modal characteristics of the conjugated structure. In the course of operation, the resonant heights are at their peak at the places of supporting. The stiffness changing changes only the plate vibration characteristics and does not affect the shell.
The obtained solution was verified by comparing theoretical results and experimental data. When conducting experimental studies, a noncontact frequency response meter of the HSV2000 system was employed. It consists of an HSV2001/2002 controller, an HSV800 laser unit and a rugged compact HSV700 sensor head. The laser unit contains an interferometer and a lowpower laser, as well as a Rohde & Schwarz RTB2002 oscilloscope.
The displacement components of a cylindrical shell and a circular plate are expanded as a rule independently from the boundary conditions as a superposition of a twodimensional Fourier series and several additional functions. The unknown expansion coefficients are treated as generalized coordinates and determined by the wellknown RayleighRitz procedure. The boundary conditions and conjunction conditions are being accounted for by employing reaction components of the hinge fastening. The acceptable accuracy of the current solutions is being demonstrated by comparison with the results obtained from the experimental studies. Satisfactory results, demonstrating the applicability of the resulting method, were obtained using the Polytec system. 
Sharunov A. V. Numerical simulation of the preforming process of a thickwalled coupling made of shape memory alloys. Trudy MAI, 2024, no 134 The work deals with the numerical modeling of the predeformation process (distribution – increase in the inner radius) of a thickwalled cylindrical coupling made of shape memory alloy (SMA) with the constant pressure in the process of direct thermoelastic phase transformation. The process of elastic, phase and structural deformations accumulation while the SMA coupling cooling through the temperature range of direct martensitic transformation was considered within the framework of the problem.
As part of the work, the process of model integrating of the nonlinear deformation during phase and structural transformations into the finite element complex Simulia AbaQus was performed through the procedure for creating custom material using UMAT technology and explicitly determining the tangent stiffness matrix. The predeformation process of a thickwalled cylindrical coupling made of SMA is being considered in a oncecohesive thermomechanical formulation, with account for the effect of the acting stress on the of phase transition temperature values.
The article demonstrates the effect of accounting for the structural transition in the process of a direct thermoelastic phase transition for two types of boundary conditions. Fidelity of the results of the work is confirmed by the validation of the developed software modules based on the results of field tests of elementary samples based on the NiTi system and verification employing known analytical solutions to the boundary value problems of the SMA mechanics.
The results presented in the article may be employed in the design of thermomechanical joint couplings from the SMA. 
Hoa V. D., Zveryaev E. M., Pykhtin A. V. Analytical solution for thermally stressed twolayer elastic strip. Trudy MAI, 2024, no 134 The article considers a thin rectangular strip response to the mechanical load impact (in the plane of the object) and a temperature field in the formulation of a plane problem of the theory of elasticity. The basis of the solution is application of the SaintVenant–Picard–Banach method for integrating the equations of the theory of elasticity of thinwalled systems (SVPB). The method combines iterative and asymptotic approaches and is of greater freedom from assumptions limiting the solution.
The first feature is transition to the sequential integration of the original equations. The relationships are being linedup in such a way that the result of the previous one is used in the subsequent expression as a known value. Introduction of the initial approximation allows considering such sequence as an iterative operator of the successive approximations method. The unknown functions selection as the initial ones, being determined (refined) in the solution process, corresponds to the idea of the semiinverse SaintVenant method, expanding its interpretation to an iterative one.
Elimination of differentiation operators with respect to the thickness coordinate in equations by integration includes in the iterative operator the integration operators correlated with the Picard operators of the method for solving firstorder differential equations resolved with respect to the derivative (which is also iterative).
Consistent application of the iterative operator gives integrals (the form of solution for the unknowns of the problem) in the form of asymptotic rads with respect to the small thinwall parameter. The solution error is being estimated by the degree of the small parameter (which is an arbitrarily small value) of the leading term of the discarded part of the series. The solution existence and uniqueness are determined by the principle of compressed mappings (Banach's fixed point theorem).
The resulting integrals (iterative approximations for the functions of the stressstrain state) are used to satisfy the boundary conditions of the problem. As the result of this, the main unknown problems are determined (the arbitrary rules of integration, which include initial approximation functions).
SVPB is an analytical method, and the asymptotic approach is also usually used to isolate from the equations the available relations characterizing the components of the solution with certain properties (in particular, quickly and slowly changing components responsible for the edge effect and the main solution). When solving the problem under consideration, the type of solution for the main unknowns is obtained by direct transformations without the use of asymptotic hypotheses. For the first iteration, a comparison with the asymptotic solution was performed. The solution is supplemented with the results obtained from the relations of the next iteration. 
Basharina T. A., Yeltsov I. S., Akolzin I. V., Kruzhaev K. V. Development of water jet ejector with a wide range of flow characteristics. Trudy MAI, 2024, no 134 The article presents the results of the development and hydrodynamic studies of the operating modes of a water jet ejector operating in a wide range of flow characteristics (3100 l/min) and representing a jet pump with axial supply of an active (working) singlephase liquid medium and radial supply of a passive (ejectable) singlephase liquid medium. In the course of a computational experiment with subsequent verification of the results with a fullscale experiment, operable and inoperable modes of operation of the device were identified, the dependence of efficiency on the values of active and passive media consumption in a wide range was obtained. The basis for the computational experiment is a geometric model of the flow area of the working fluid, in which the simulation of the area of reduced pressure in the receiving chamber occurs by the outflow of the active medium at high speed through the working nozzle and subsequent pumping of the ejected medium. Of the 25 designs of the water jet ejector, the most promising one was selected, the confirmation of the operability of which was carried out in 9409 operating modes. Several main structural elements have been identified, each of which, as it was found, significantly affects the functioning of the device. The conducted research allowed us to identify practical recommendations used in the development. In the verification process, the difference between the computational experiment and the fullscale one was established, not exceeding 5%, which corresponds to sufficient engineering accuracy. The high degree of reliability of the results obtained, confirmed by field tests, allows the use of this water jet ejector of the developed design in the task of pumping media with a wide range of volumetric flow rates. 
Prokopenko E. A., Gerasimenko E. Y. Investigation of the process of fuel outflow from the centrifugal nozzle of a liquid rocket engine. Trudy MAI, 2024, no 134 The article presents a study of the consumption characteristics of a centrifugal nozzle by numerical modeling methods using the ANSYS CFX software package with verification of the results obtained by the method of spills used by the component of rocket fuel.
Numerical studies were carried out in the ANSYS CFX software package to determine the nozzle spray angle. A threedimensional model of a centrifugal nozzle was developed as an object of research.
Similar studies were carried out at various pressure drops on the nozzle using expressions for the flow coefficients of an ideal centrifugal nozzle (µ_{f}) with a tangential inlet.
Measurements of the volume of liquid fuel flowing out over a certain period of time were carried out with a corresponding pressure drop in the fuel tank and the environment to determine the mass flow through the nozzle. Pressure losses in the fuel line were previously measured, taking into account local resistances and losses along the length of the pipeline lines. Accounting for pressure losses is necessary to ensure the specified accuracy of determining fuel consumption through the nozzle. Alcohol is used as a fuel of a given concentration at the current values of ambient temperature and pressure. These data made it possible to calculate the fuel density and its kinematic viscosity coefficient.
Analysis of the values of the coefficients of mf obtained by experimental and computational methods shows that the theoretical value of µ_{f} for an ideal centrifugal nozzle is significantly less than the real value. The values of µ_{f} are constant at different values of the pressure drop at the nozzle, with the same geometric parameters of the nozzle. These differences are beginning to manifest themselves to a lesser extent in terms of mass expenditures.
The results of the conducted studies show that the flow characteristics of a real centrifugal nozzle may differ from the ideal one. On the one hand, this contradiction is due to the deviation of geometric characteristics from nominal values during the manufacture of nozzles and the geometric parameters of the flow sections and the location of sensor equipment on the pouring stand, on the other hand. This leads to the fact that it is necessary after the manufacture of the nozzle to carry out its spillage in order to clarify the design values of the consumption characteristics in the end. The results obtained can be used in the development of the technological process of manufacturing new injectors and refining defective ones. 
Khatuntseva O. N. Accounting for entropy production in the liouville equation and the derivation of a "MODIFIED" system of navierstokes equations from it. Trudy MAI, 2024, no 134 Turbulent and laminar flow regimes of a liquid or gas are indistinguishable on the scale of thermal motion of molecules. However, there are significant differences between them on the meso and macroscales. The turbulent regime has the features of a stochastic time–irreversible process at all scales of consideration, moreover, stochastic pulsations in the turbulent regime at different scales are correlated – they have a collective character. In contrast, the laminar regime is deterministic and timereversible at all scales significantly exceeding the scale of thermal motion of molecules. There are ranges of parameters above some critical values at which both laminar and turbulent modes can be realized and exist with different probabilities. Transitions between them occur abruptly, irreversibly, that is, the reverse transition when changing parameters in the opposite direction can occur (and usually does) at other parameter values. Thus, an equation describing both of these modes should allow for a nonunique solution, with an illsmooth and ambiguously defined transition between them.
Earlier, studies were conducted on the possibility of describing both laminar and turbulent fluid flow based on the same “modified” NavierStokes equations, which take into account entropy production in the turbulent regime due to the excitation of stochastic disturbances at different flow scales [14].
Solutions corresponding to laminar and turbulent flow regimes of an incompressible nonthermally conductive liquid were analytically obtained for the HagenPoiseuille problems, the Poiseuille plane flow and the Couette plane flow. Experimental and analytical solutions for different values of the Reynolds number are compared.
This paper shows the possibility of moving from the Liouville equation, which takes into account the production of entropy at different scales (the “modified” Liouville equation) to the “modified” Boltzmann equation through a chain of “modified” Bogolyubov equations. Based on these equations, a “modified” system of NavierStokes equations is derived. 
Nikolsky A. A. Helicopter airfoil design using the PGT technique. Trudy MAI, 2024, no 134 The purpose of the presented work consists in creating prospective approach to the airfoil design. A technique with no analogues, namely PGT (parent function generating) technique, which represents a universal geometry parameterization tool and ensures design space in the form of physical region on a plane, bounded by the two monotonous curves, is used for this purpose.
This tool is being combined with the solvers of various accuracy to exploit its advantages. The other purpose consists in studying the contour approximation accuracy to determine the necessary number of the design variables enough for the airfoil aerodynamic design.
Methodology consists in applying the PGT technique, including generating functions, a universal parent function and the two extra parameters to the aerodynamic design problem. At the start, the initial design space is reduced by employing the lowlevel substantiated solver for local optimization problems solving. Then the process is continuing in reduced space with the highlevel solver. Two types of the generating functions approximation are being discussed for the number of the design variables selection.
As the result, the twostep procedure is appeared to be much less consuming than the singlestep one. It requires about 100 iterations with high estimated cost and about 1000 iterations with low estimated cost.
Despite this, the demonstrating example of helicopter airfoil design demonstrates the possibility of significant improving of the targeted aerodynamic performance.
The presented study revealed that the original PGT technique allowed significant improvement of the results achieved at the previous level of the aerodynamic design, and, probably, achieving an optimum near the global optimum. In conjunction with the twostage strategy, it significantly enhances computational effectiveness of the aerodynamic design procedure.
The fact that the PGT technique may be applied in the 3D problems for aerodynamic objects of the wing or fuselage type seems to be of great importance. 
Abramov M. A., Arefiev K. Y., Voronetsky A. V., Sarkisov A. V., Grishin I. M., Kruchkov S. V. Computational and experimental research of the gas dynamic factors’ impact on the stochasticstatistical dispersion of particles in a twophasr highvelocity flow. Trudy MAI, 2024, no 134 The present study explores the gasdynamic factors impact, specifically directed injection, on the empirical coefficients used to convert discrete particle trajectories into a locally continuous field of the dispersed phase flow intensity in supersonic turbulent twophase flows. Statistical modeling is employed to develop a technique for the particle localization distribution evaluating, with account for the probabilistic nature of the trajectory deviations.
A discretecontinuous transformation method is applied by constructing a probability density function to evaluate the particle localization distribution. This technique assumes that the cluster velocity vector deviation from the section normal is negligible. By utilizing this probability density function, an equation is derived to convert discrete particle trajectories into a continuous field, approximating a twodimensional normal distribution. The flow rate intensity, defined as the ratio of the particles mass flow to the unit area, is used to create a continuous field of particle flow intensity distribution. The basic trajectories of cluster motion are computed with the LagrangeEuler method. A supersonic experimental setup for gasdynamic spraying of coatings is employed to determine the the normal distribution value and examine the particles spatial localization.
The experimental data reveles that the acquired volumetric layer of sprayed condensed phase indicates the particle distribution structure in the crosssection of a highspeed twophase flow.
The main findings of the study demonstrate that random factors significantly affect the particle distribution in the flow. The standard deviation of particle spatial localization ranges from 4.8 to 5.4 mm for a dispersed phase size of 15 to 40 μm in a supersonic flow, regardless of the presence or absence of a drifting flow. 
Golovkin M. A., Grudinin M. V., Efremov A. A., Mirgazov R. M. Aerodynamic drag coefficients of circular cylinders of finite elongation at low subsonic speeds. Trudy MAI, 2024, no 134 The introduction presents a review of the literature on the considered subject. It is noted that in accordance with the previously obtained data for the c_{x}(Re), namely the dependence of the drag coefficient of a circular cylinder of relatively large aspect ratio λ = 17.8 (λ = L/d, L – cylinder length, d – its diameter) on the Reynolds number (Re = V·d/ν, V – flow velocity, ν – coefficient of kinematic viscosity of air), the transition mode from the laminar separation to the turbulent one is close to that of cylinder with infinite aspect ratio, and for the cylinder with λ = 9.2 it is noticeably lagged by the speed value, or Re number.
This is of practical importance, in particularl for the spin simulation in a wind tunnel (WT) with aircraft models, to know whether this trend holds for the cylinders of lower aspect ratio, which are usually used in typical fuselages of modern longhaul aircraft (λ = 6 ÷ 8). In this regard, this study considered the aspect ratio of λ = 6.15.
The tests were conducted in a vertical WT with a sufficiently low degree of the flow turbulence, within the speed range of V = 3 ÷ 33 m/s by increasing and decelerating speed with a pitch of 2 m/s.
This presented study confirmed a significant lag by the Re number for the laminar separation mode of relatively low aspect ratio, compared to an infinite cylinder.
The article demonstrates that transition to the turbulent separation at the cylinders of relatively low aspect ratio occurs in a much narrower range of the Re numbers than with an infinite cylinder.
A hysteresis in the drag coefficient while increasing and decelerating speed exists in the region of Re numbers corresponding to the transition mode from laminar separation to the turbulent one.
The drag coefficients values of the finite aspect ration circular cylinders in the ranges of Re numbers corresponding to laminar separation obtained in the vertical WT agree satisfactorily with the data available in the known literature.
The detected effects and the presented results should be accounted for when developing and conducting studies with aircraft models in the WTs. 
Le V. H., Frolov V. A. The influence deflectors located near cylinder on drag of combination «cylinderplates». Trudy MAI, 2024, no 134 The study of the flow around the circular cylinder is one of the most uptodate fluid and gas mechanics problems due to its wide application in industry. Here are some examples: wind turbines, towers, highrise buildings, offshore structures, industrial chimneys and bridge hanger cables. Drag reduction of the cylindrical objects in aviation has been of great interest of many scientists for a long time. Various active and passive methods were applied earlier for the cylinder drag reduction. Active methods are being characterized by their effectiveness and by the fact that they require energy supply from the outside. Passive methods are based on adding extra bodies near the cylinder or geometry changing the cylinder surface, thus, unlike the active methods they do not require energy supply. The basic principle of these methods consists in moving the separation point back downstream, since later separation of the flow leads to the drag force reduction.
This work studies a passive drag reducing method through installing flat plates near the cylinder. The modeling problem was restricted by the twodimensional case. Velocity and pressure fields near the cylinder, as well as drag coefficient dependencies on the number and relative lengths of deflectors were obtained with the ANSYS Fluent software. The authors found that the drag coefficient of the cylinder combination with one flat deflector and fixation of the back partitioning plate, situated in the horizontal plane of symmetry may reduce significantly the drag coefficient down to minimum value of 0.45.
The data presented can be recommended for the aerodynamic design of the bodies with cylindrical cross section for the drag reduction. 
Fedorinov A. Y., Ivanov Y. P. Investigation of the universal optimal method of finitetime and spectralfinite processing of navigation signals of aircraft instruments in conditions of complete and incomplete a priori certainty. Trudy MAI, 2024, no 134 In the theory of measuring information processing, new approaches have been developed to finitetime and spectralfinite methods of signal processing (filtering). The signal filtering procedure is the most important task in the field of information processing. The article will explore the key features of these algorithms. These approaches are based on the orthogonal projection theorem and are optimal by the criterion of the minimum amount of error variance. The approaches are capable of producing linear recurrent estimates of nonMarkov signals with correlated and uncorrelated interference. At the moment, the engineering community is making extensive use of Kalman filtering. The proposed algorithms will have an advantage over the Kalman filter. The estimation algorithms obtained on the basis of this approach coincide in accuracy with Kalman filtering and are applicable to a wide class of signal and interference models. In this paper, recurrent sums of error variances of current and interpolated estimates, optimal by the criterion of minimum, linear algorithms for filtering signals under conditions of various a priori certainty against the background of correlated and white noise, with memory provision for the measurements obtained from the beginning of work, will be investigated. The optimal estimation algorithms obtained on the basis of the properties of the orthogonal projection theorem are universal for a wide class of signal and interference models, independent of the presence of the markovity property of the signal and the correlation of measurement interference, coinciding in accuracy with Kalman filtering, simpler in their implementation, due to the adaptability property, they have increased noise immunity and robustness, at the same time With optimal filtering, optimal signal interpolation is provided The simulation was carried out in the Mathcad environment. Currently, the following algorithms have been implemented and studied: finitetime and spectralfinite; with/without feedback; adaptive / nonadaptive; with or without known interference, and their combinations. 
Aliyeva G. V., Huseynov O. A. Issues of building an adaptive flight mode of a reconnaissance UAV. Trudy MAI, 2024, no 134 The need for a correct assessment of the effectiveness of the conducted reconnaissance carried out using integrated spatially distributed aviation complexes of manned aerial reconnaissance facilities is explained by the extreme conditions in which they often have to be implemented. At the same time, proper planning of such flights is one of the most important tasks, the solution of which would ensure the successful completion of the mission of unmanned aerial vehicles of the reconnaissance type. Taking measures to ensure the high quality of images obtained during the flight of the UAV is certainly an essential component of such planning. images. The purpose of this study is to determine the main patterns in the organization of an adaptive mode of operation of optoelectronic reproducing equipment. The essence of the proposed adaptive mode is to promptly change the focal length depending on the altitude of the UAV in order to achieve the maximum possible value of the indicator on the NIIRS scale. Currently, the NIIRS criterion is used to evaluate the quality of images obtained from electrooptical UAV systems in the infrared range. NIIRS is an evaluation scale of the degree of interpretability of images received from UAVs. The higher the NIIRS score, the more details you can make out in the resulting image. The NIIRS scale contains 10 levels, where the zero level indicates an image in which it is impossible to distinguish any details, the ninth level indicates images in which the movement of people is clearly visible. The mathematical apparatus most often used to calculate the levels of this scale is the General Equation of Image Quality. The possibilities of adaptive construction of reconnaissancetype UAVs with variable focal length are investigated. It is shown that the root dependence of the second degree of the UAV flight altitude on the focal length of optoelectronic equipment is the worst option for adaptive flight altitude control, when implemented, the evaluation of the UAV mission on the NIIRS scale reaches a minimum value. When designing and operating an intelligencetype UAV, it is advisable to avoid organizing such an adaptive control mode. 
Emelyanov A. A., Unchenko I. V. Research of the layout of a promising system for synchronization of diversity receiving channels of a radio interferometer using microwave photonics technology. Trudy MAI, 2024, no 134 Highprecision measurement of the angular coordinates of radio emission sources is the cornerstone task of modern digital radio interferometers. The main measured parameter in these devices is the totality of the phase differences of the signal received and digitized by spaced receiving channels. To achieve high measurement accuracy, it is necessary first to minimize the differencephase errors in digitizing the received signal by spaced receiving channels. In addition, the placement of radio interferometers at most objects involves solving the problems of minimizing the size of the system, its weight, power consumption and cost. To optimally solve these problems, it is proposed to use fiberoptic communication lines (FOCL) with their own low phase noise, which is based on modulation of laser radiation through electroabsorption.
The purpose of this work is a practical assessment of the degree of influence of the noise characteristics of a fiberoptic link, which is based on the modulation of laser radiation through electroabsorption, on the quality of the synchronization system signal and a comparison of the calculated and measured noise and transmission characteristics of the transmission path of the synchronization system of spaced receiving channels of a fiberoptic interferometer radio interferometer.
The object of study was: a model of the transmission path of the synchronization system (hereinafter referred to as the system). The research was carried out using a calculationanalytical method and through practical measurements using a phase noise analyzer, a network analyzer, and a signal analyzer.
During the work, transmission and noise coefficients for the system were calculated. Taking into account the amplifiers used, the calculated value of the transmission coefficient was no more than 16 dB and no less than 24 dB for the noise figure. According to the measurement results, the transmission coefficient was from 13 to minus 3 dB, and the noise figure was at least 30 dB; the resulting discrepancies are due to the nonlinearity of electrooptical conversion through electroabsorption and the nonlinearity of the photodiode. The introduced phase noise of the synchronization system was measured at frequencies of 1, 5 and 10 GHz. The value of the introduced phase error of the fiberoptic communication line was determined, which was: for 1 and 5 GHz  no more than 0.056 degrees, and for 10 GHz  no more than 0.176 degrees. 
Koval N. A. Comparative analysis of neural network architectures in the task of detection and identification of target and velocity jammer signals. Trudy MAI, 2024, no 134 As is known, radar signals are subjected to various kinds of interference. A special place is occupied by the imitating interference to automatic tracking systems (leadingastray interference). The means for the leadingastray interference creating are capable of generating signals, which smoothly introduces false information about the target movement parameters (such as Doppler frequency or delay time), which ultimately leads to the automatic tracking failure [12].
Velocity leadingastray jammers (VJ) represent the greatest danger for the onboard Doppler radar stations. The jamming effect file detection and jamming and target signals distinction at the initial stage of the jammer operation, which would prevent the traction failure and ensure reliable information obtaining about the target, may be solution to the problem of the VJ counteracting. The capabilities of artificial neural networks (deep learning) are being studied in the presented article for this problem solution. The idea consists in regularities educing by the neural networks in characteristic dynamics of the signal spectrum received by the radar system under the imVJ pact of the in the process of their learning.
Temporal interrelation of the spectrums, obtained at the successive radar station operating cycles, should be accounted for the characteristic dynamics educing, which brings us explicitly to the time sequences processing task. As long as the very fact of the interference impact educing is understood as the VJ signal detection task, this can be represented in the context of machine learning in the form of the spectrum classification task (spectrum transformation of the signal received at every cycle of the radar operation into the VJ presence/absence mark). The signal frequency estimation in its turn is being reduced to determining the index number of the Doppler’s filter, which in their essence are the frequency domain sampling. That is, each filter is assigned a certain frequency range of the signal being analyzed at a given time instant. Thus, this task can be represented as a spectrum regression (converting the spectrum into the number of the Doppler filter of the target signal).
The following architectures intended for thetime sequences processing are being studied within the framework of this article: classical convolutional CNN network (for working with time sequences, layers of onedimensional convolution are employed) [7]; temporary convolutional TCN network [8]; recurrent networks based on the LSTM long shortterm memory layers [9]; networks based on managed recurrent GRU units [10]. Several models of each presented architecture were trained with different number of layers, size of layers, etc. To assess the trained models quality, the root of the mean square error (RMSE) for the regression problem and the Fmeasure (F1score) for the classification problem were applied.
The result of the accuracy comparing of the considered architectures reveealed that CNN displayed the worst result of 6.3 RMSE and 0.986 F1score. TheLSTM and GRU appeared to be the most accurate in both tasks (1.23 RMSE and 0.997 F1score, 1.27 RMSE and 0.995 F1score, respectively), and in the classification task, they apparently reached the limit of accuracy. TCN performed slightly worse (1.45 RMSE and 0.994 F1score), however, the required network size to achieve results comparable to LSTM and GRU makes the use of TCN impractical.
The author recommends employing the LSTM or GRU network with two layers of 100 hidden units for regression and an LSTM with two layers of 25 hidden units for classification in the considered task. The choice between architectures is being stipulated by the required level of accuracy and hardware limitations on the counteraction algorithm being developed: the LSTM is slightly more accurate, but due to its structure ,it has more trainable parameters with the same number of hidden units, which leads to the use of more memory and lower computing speed compared to GRU.
Thus, the article demonstrates that neural networks are able to solve the said problems quite accurately. In the course of the study, a comparative analysis of neural network architectures designed for processing time sequences was performed and suitable for further integration into onboard digital signal processing algorithms were identified.
The author’s further intention is to study the selected architectures structures in the more complicated jamming situation. 
Semenov A. S. Simulation of bell states for the software implementation of a quantum simulator. Trudy MAI, 2024, no 134 The aim of this study is to enhance the efficiency and precision of quantum simulators via the simulation of Bell states utilizing diverse quantum gates, initialization, and measurement algorithms. Such research will enable us to gain a more profound comprehension of quantum solutions for intricate issues while enhancing their performance.
Bell states are a set of four entangled quantum states represented by two qubits. Each qubit can be in a superposition of two states, namely 0 and 1. These states are used as building blocks for many quantum algorithms and quantum protocols, such as teleportation and dense coding. Bell states are also used to experimentally demonstrate quantum entanglement and quantum teleportation.
Theoretical modeling of Bell states requires understanding the quantum state correlations between two qubits in an entangled state. Let us highlight three approaches to simulating Bell states: algorithms based on various quantum gates, algorithms based on density matrices that describe the statistical properties of quantum systems, and algorithms based on entanglement measures that quantify the degree of entanglement between two qubits.
Understanding the effects of noise and imperfections in quantum hardware for entangled state generation in Bell state simulations requires the development of error correction and fault tolerance methods for quantum information processing. Research into multiqubit entangled states demonstrates complex quantum phenomena such as quantum teleportation networks and quantum error correction codes.
The following algorithms simulating Bell states are considered: an algorithm based on the Hadamard and CNOT gates, an algorithm using a singlequbit PauliX gate, an algorithm using a singlequbit Sgate, an algorithm using a Tgate, an algorithm using an Xgate,
The initial state generation algorithm prepares qubits for quantum operations and measurements. The correct choice of the initial state can influence the results of calculations and the efficiency of the algorithm. In addition, the measurement results depend on the states of the qubits after performing quantum operations. Let's take a closer look at these algorithms.
The algorithm for generating multiple random initial states of a twoqubit system is useful for testing the behavior and stability of quantum algorithms and simulators. The Kronecker product of qubit states allows the algorithm to represent the entire state of two qubits as a 4dimensional vector, which is used to model the evolution of a quantum system over time.
When measuring the states of a twoqubit quantum system in the Bell basis, the measurement probabilities give an idea of the chances of different measurement results. These probabilities are calculated based on algorithm nqubit measurements. By measuring the system several times and comparing the measured results with the probabilities, the quantum mechanical predictions and the accuracy of the quantum device are checked.
The proposed algorithms improve the simulation and manipulation of Bell states, making them suitable for a wide range of applications, particularly the enhancement of software implementations of quantum simulators. This study was focused on improving software quantum simulators, providing an advancement in the field. The significance of Bell states for quantum information and computing is emphasized in the paper, along with the necessity of accurate and efficient simulation and manipulation of these states. 
Blinkova O. V., Kondratov D. V. Modeling the dynamics of interaction of a compressed layer of a viscous compressible liquid with an elastic threelayer stator. Trudy MAI, 2024, no 134 With the constant development of mechanical engineering, space and aviation industries, the tasks of investigating the interaction of two elastic plates with a viscous liquid or gas between them are becoming more and more urgent. The study of elastic plates, the space between which is filled with a viscous liquid or gas, is becoming increasingly necessary. A mechanical system consisting of two plates interacting with each other through a layer of viscous compressible fluid in which constant pressure is maintained, as a result of which the upper absolutely rigid plate performs vertical oscillations is considered. The first plate is absolutely rigid  the vibrator, the second  is an elastic threelayer plate  the stator. The mathematical model in dimensionless variables is a coupled system of partial differential equations describing the dynamics of the motion of a viscous compressible fluid (NavierStokes equations and continuity equation) flowing between two plates with the corresponding boundary conditions. To solve the resulting problem of the interaction of a viscous compressible fluid and an elastic threelayer plate, we switched to dimensionless variables of the problem. Small parameters of the problem were chosen  the relative width of the viscous fluid layer and the relative deflection of the elastic stator. The selected small parameters of the problem made it possible to use the perturbation method to simplify the system of equations. The BubnovGalerkin method has found an expression for the amplitudefrequency characteristics of an elastic threelayer stator, further study of the expression will allow to identify and exclude resonant phenomena in structures of this type, take them into account when building new structures in modern mechanical engineering, aviation and space industries. 
Goncharova V. I. Parametric synthesis of a nonlinear automatic control system with distributed parameters. Trudy MAI, 2024, no 134 The development of an automatic control system for any fairly complex technical object is a long, multifaceted process; one of the main stages is the construction of an adequate mathematical model of the control object. The choice of a mathematical model of an object is in one way or another connected with the idealization of its mathematical description, which involves highlighting the main patterns in the behavior of the object and neglecting secondary connections and effects, taking into account the expected conditions of its physics of functioning in a real system. In this work, we will consider an example related to temperature control in a furnace. Since in such a system it is necessary to take into account several variables, when constructing a mathematical model, the automatic control system is distributed. If, in a system for regulating the heating of a rod in a furnace, we implement the transition from partial differential equations inherent in systems with distributed parameters to ordinary differential equations, then it is most advisable to consider the system as a linear system with a retarded argument.
It should be noted that such a procedure is very useful, since algorithms for efficiently solving ordinary differential equations are much better developed compared to algorithms for directly solving partial differential equations.
The paper presents a possible implementation of the transition from partial differential equations to ordinary differential equations for solving the problem of parametric synthesis using the generalized Galerkin method for automatic control systems with distributed parameters. As a mathematical apparatus, the method of separation of variables (Fourier) is used, as well as obtaining state space matrices in order to obtain the transfer function of an automatic control system with distributed parameters. 
Vataeva E. Y. Parametric synthesis of a lowpower potentiometric tracking system. Trudy MAI, 2024, no 134 Currently, the most rapidly developing areas of research in the theory of automatic control are nonlinear and stochastic analyses. This interest is justified by the fact that most physical processes in nature and systems in the real world are nonlinear and are also subject to random disturbances, i.e. stochastic. In modern automatic control theory there are a large number of methods and studies devoted to the synthesis of nonlinear automatic control systems, but no unified approach has been developed that would allow the synthesis of nonlinear automatic control systems of any complexity. Also, difficulties in solving the problem of synthesizing nonlinear automatic control systems also arise when constructing an adequate mathematical model, since this issue is related to the idealization of the properties of both the elements of the control system and the automatic control system as a whole. It is known that when constructing a mathematical model, all the basic and most essential features and properties of the synthesized ACS must be preserved; in the presence of nonlinear elements in the ACS, this situation is associated with the choice of the correct choice of approximation [110]. As is known, there are various types of approximations of the characteristics of nonlinear elements, for example, analytical, power, piecewise linear, approximation by irrational functions. However, for accurate implementation of a nonlinear characteristic with piecewise linear approximation, it is necessary to increase the number of piecewise linear sections, which leads to complication and an increase in the synthesis time of such a system. With analytical approximation, it is quite difficult to instantly obtain the correct analytical expression. In this work, it is proposed to use polynomial approximation. As a mathematical apparatus it is proposed to use the generalized Galerkin method. 
Tarasov D. Y., Sukhomlino G. L., Mikhailov V. V. Numerical modeling of transient and steadystate modes in the operation of pulsed DCDC voltage converters. Trudy MAI, 2024, no 134 It is noted in the introductory part of the article that approaches based on application of the powerful commercial software such as MATLAB/Simulink are widely employed in the research works of the design organizations associated with the various types of the switchedmode DCDC voltage converters development. At the same time, the trend associated with development of simpler computing tools, which can be relied upon not only while conducting specific computational studies of the said converters, but also for reliability confirming of the results obtained based on this software as well, is still being called for. The purpose of the article consists in describing one of the like type of computational tools based on the numerical integration method and designed for studying transient and steady state operation modes of the converters under discussion.
The article points out that systems of differential equations describing the dynamics of the switchedmode DCDC voltage converters are characterized by the presence of specifics associated with abrupt changes of their parameters in time initiated by switching by pulsewidth modulators with a given clock frequency f and a period T = 1/f. With reference to the work of one of the coauthors of the article, dealt with the numerical solution of dynamics problems of the electromechanical systems with discontinuous features (such as dry friction), the authors note that a simple and effective way of numerical implementation in such cases is application of an unconditionally computationally stable implicit Euler scheme when integrating over time.
The main content of the article deals with the description of the said approach in relation to the numerical simulation of transients in the operation of a buck switchedmode DCDC voltage converter. The article presents a design diagram of the converter and corresponding dynamics problem is formulated in the form of a system of the two firstorder differential equations (with respect to the inductor current i and the load voltage U) with discontinuous features. The algorithm of the numerical solution, implemented in the form of a program in the Fortran language, is recounted. The article presents the results of computations performed by this program related to the transient operation modes of the two concrete buck converters. These results fidelity is confirmed by comparison with the simulation results available in the open sources, performed in the MATLAB/Simulink. The article points at the option of the proposed model application (accounting for the discontinuous specifics) in the version corresponding to the socalled “continuous” or “averaged” model. On the example of the transient process computing for one of the considered buck converters performed with “discontinuous” and “continuous” versions of the developed computational model the article demonstrates that computational results of these versions are in good agreement with each other.
The final part of the article contains conclusions on the research performed. It is noted here that the article presents (based on the implicit Euler scheme implementation) an approach to the numerical modeling of transients of the switchedmode DCDC voltage converters operation, with account for discontinuous features in the formulation of differential equations describing dynamics of such devices. Transients of two options of the DCDC buck voltage converters (described in literature) were subjected to the numerical analysis. Fidelity of the numerical simulation results has been confirmed by practical concurrence with the results of computer modeling and physical experiment available in the literature. Capabilities of the continuous version of the developed computational model for solving problems of dynamics of the buck switchedmode DCDC voltage converters have been demonstrated. 
Uryupin I. P. Modeling and assessment of connectivity aviation and railway passenger transportation systems of the Russian Federation. Trudy MAI, 2024, no 134 An important component of the country's socioeconomic development is the presence of a developed multimodal transport system. One of the main tasks of the effective functioning of such a system is consistency with each other individual modes of transport. It makes possible to increase transport accessibility for potential passengers in the system.
The purpose of the study is to assess connectivity of the aviation and rail transport systems of passenger transportation in the Russian Federation. In Russia, it is not possible to talk about a unified transport system, due to the geographical features of the country. But it is also impossible to consider these systems completely unrelated, because in large metropolitan areas of the country, these types of transport closely interact with each other. Therefore, for the effective development of the multimodal transport system of the Russian Federation, it is necessary to take into account for which flight points there is an alternative mode of transport (railway), and for which flight points aviation is the only transport for transportation or it can serve as a feeder transport to railway stations. To solve this problem, a model has been developed that allows us to determine the availability of railway communication for each flight point.
The first section provides a description of the initial data for modeling, and the software implementation of their automatic collection.
In the second section, based on the collected data, a methodology has been developed according to which flight points are divided into 5 structural groups according to the presence and accessibility alternative mode of transport  railway. A “special” group of flight points has been identified, for whose lives air transport is important.
The third section provides an analysis of the results obtained. Populated areas have been identified (including the number of potential passengers in them) from which departures could theoretically be to the transport passengers to railway stations, thereby increasing the connectivity of transport systems. 
AlMaliki M. N., Yuferev L. Y., Yakimovich B. A., Kuvshinov V. V. Passive cooling effects of silicon photoelectric cells and their behavior. Trudy MAI, 2024, no 134 Application of photovoltaic converters for the aviation and space industries represents a very important task. In particular, it is the main source of electrical energy at space vehicles and stations. Certain drawbacks constantly arise herewith during the semiconductor photocells operation. The authors of the presented article propose several solutions to this problem. The photoconverters overheating, for example, leads to their efficiency degradation and energy characteristics deterioration. For this problem solving, the authors proposed an interesting technique for the said consequences mitigation. Theoretical and experimental studies were conducted, the necessary computations were performed and qualitative proposals were made during this work. The presented study analyzes the effect of passive cooling on the efficiency of the siliconbased photovoltaic cells. The photovoltaic cell (PV) was subjected to heat dissipation through the aluminum heat sink. The radiator sizing is based on the results of the stationary heat transfer analysis. The experimental studies were conducted at various ambient temperatures and illumination levels up to one sun with a sun simulator. Based on the empirical data obtained by applying this cooling methodology, the photovoltaic cell efficiency in converting light energy into electrical energy is greatly improved. The efficiency of the photocell increases by 20% when exposed to radiation with an intensity of 800 W/m^{2}. The most significant temperature reduction is being noted at an illumination level of 600 W/m^{2}. Photovoltaic cells, both with and without fins, demonstrate improved performance at lower ambient temperatures. The studies being performed allow ensuring highquality generation of the electric energy and reducing the dependence of the solar panels operation on temperature, which significantly improves the energy characteristics of the power plant and ensures reliable electrical energy generation. Theoretical and experimental studies performed in the course of this work allow continuing the solar installations development and may significantly expand scientific data on the operating modes of photovoltaic stations, both groundbased and spacebased. This data is necessary for both ensuring reliable operation of aerospace equipment and for the groundbased power systems operation. 
Makeev P. A., Chermoshentsev S. F. Testing the method of automated placement of elements on a rigidflexible printed board using practical examples. Trudy MAI, 2024, no 134 The use of rigidflex printed circuit boards on aircraft is due to the necessity of reducing overall dimensions and its weight. However, the use of rigidflex printed circuit boards leads to problems of with thermal and electromagnetic compatibility due to the high density of elements on the board.
This article proposes the use of a technique for automated placement of elements on a rigidflex printed circuit board of an electronic device, taking into account thermal and electromagnetic compatibility based on a twolevel genetic algorithm.
The technique includes two levels of placing elements on the printed circuit board. At each level of the methodology, when solving the problem of automated elements placement, a modified genetic algorithm is used. The first level of the technique consists of super elements placement (an active elementmicrocircuit and associated passive elements) on a rigidflex printed circuit board, taking into account the criteria of thermal compatibility and a minimum of total weighted length. The second level of the technique ensures the elements placement on the printed circuit board within a super element, taking into account the criteria of electromagnetic compatibility and the minimum of total weighted length. Verification of the obtained solutions is achieved through the use of computer modeling tools at each level of the proposed methodology. This ensures thermal and electromagnetic compatibility on the rigidflex printed circuit board.
Validation of the developed methodology on a real practical example confirms its effectiveness and the quality of the results of elements placement on a rigidflex printed circuit board. A summary of practical examples demonstrates the possibility of using the developed methodology for the printed circuit boards design, as a special case of rigidflexible printed circuit boards. 
Anisimov S. A. Numerical analysis of buckling under axial compression of orthogridstiffened cylindrical shells made of aluminum alloys. Trudy MAI, 2024, no 134 In the introductory part of the article, it is noted that orthogridstiffened (reinforced on the inner surface by an orthogonal mesh of ribs) cylindrical shells made of aluminum alloys are widespread structural elements of rocket and space technology products, which under operating conditions are subject to large axial compressive loads. An important (in terms of strength) problem here is the calculation of this type of shell for buckling (or loadbearing capacity). Such calculations are usually performed using wellknown commercial finite element systems. The corresponding computational models are built using both shell and volumetric elements. It is noted that the use of these detailed finite element models when carrying out the necessary parametric studies may turn out to be ineffective due to the large expenditure of computer time on the calculation of a separate option. This especially applies to cases of largesized structures. Recent publications are pointed out, in which calculations for the buckling of the type of shell under consideration are carried out within the framework of models based on the “smearing” hypothesis. With this approach, the shell, supported by a network of ribs, is approximately considered according to the scheme of an axisymmetric structuralorthotropic shell, which makes it possible to construct a more computationally efficient calculation model. It is noted that in this article, a similar calculation model is constructed based on the numerical integration method.
The main content of the article is devoted to the description of the designated computational model and the calculated results obtained using it. Assuming that the reinforcing ribs are located quite often, using the “smearing” hypothesis, the ribbed cylindrical structure under consideration is reduced to a design of a structurally orthotropic shell, working in accordance with the KirchhoffLove hypotheses. The problem of buckling under axial compression of the shell model accepted for consideration is formulated in the traditional Eulerian (bifurcation) formulation, taking into account the linearity of the subcritical stressstrain state. The resulting linear homogeneous boundary value problem for a system of eight firstorder ordinary differential equations (as a result of applying the procedure of expansion into Fourier series along the circumferential coordinate) for each harmonic number n is solved using the orthogonal sweep procedure of S.K. Godunov, including numerical integration according to the KuttaMerson scheme. The numerical solution algorithm developed (in the form of a Fortran program) determines the harmonic number n and the smallest (critical) value of the compressive load Q, at which the specified homogeneous boundary value problem has a nonzero solution.
In order to check the reliability of the results obtained using the described computational model, a calculation of an axially compressible cylindrical orthogrid stiffened shell was carried out and a comparison was made with the known solution obtained using a finitedifference computational model. Additionally, an alternative finite element model was built in the MSC Patran/Nastran software package based on a tetrahedral element (Tet10). A practical coincidence of the results of the buckling calculations using all three of these computational models was noted.
Next, the question is considered concerning the degree of consistency with experiment of the buckling calculation results obtained using the developed computational model. Calculations were carried out to determine the critical loads for nine different structures of samples of orthogridstiffened shells (made of aluminum alloy) that passed axial compression tests. A slight overestimation (by about 20%) of the calculated values of critical loads compared to the experiment was noted. The analysis carried out for the considered set of samples established the desired value of the “knockdown factor” in the form k = 0.75.
The final part of the article contains conclusions on the research performed. It is noted here that the article presents a computational model constructed using the “smearing” hypothesis and the numerical integration method for calculating the buckling of axially compressed cylindrical orthogridstiffened shells. The main results obtained using the developed model are also indicated. 
Hoa V. D., Zveryaev E. M. Analytical solution for thermally stressed twolayer elastic strip. Trudy MAI, 2023, no 133 The authors consider the problem of the stressstrain state determining of a twolayer elastic strip staying in a temperature field under the action of a transverse bending load. Certain conditions may be imposed on the displacement or stress at the short sides of the strip.
A method called in [1] the SaintVenant–Picard–Banach (SVPB) method is used to construct a solution. Being based on a generalization of the ideas of the SaintVenant semiinverse method [2] and the Picard method of successive approximations of [3], it allows finding all the unknowns for a system of equations of the elasticity theory by sequential calculations without any preliminary hypotheses. The dimensionless partial differential equations with a small thinwalled parameter for a thin strip are being written as integral ones with respect to the transverse coordinate, similar to what is done in the Picard method. Next, the equations and transformed elasticity relationships are being arranged in a sequence that, accordingly, allows sequentially calculate the unknown problems, expressing them through the four arbitrary functions of the longitudinal coordinate obtained by integration along the transverse coordinate and integral coefficients from the function of changing the stiffness of the layers in the transverse direction. Having these formulas for all the unknowns of the problem being searched for, the expressions for the boundary conditions on the long sides to determine four arbitrary integration functions according to Picard [4] may be written. These expressions represent ordinary differential equations with small parameters for derivatives with respect to the longitudinal coordinate. Their solutions are slowly changing functions of the main stressstrain state and rapidly changing functions such as the edge effect. The integration constants for both solutions are being determined from the boundary conditions on the short sides of the strip. For slowly changing ones, the conditions coincide with the classical ones for a beam. The conditions unsatisfied by the classical solution are being satisfied by the integration constants of rapidly changing solutions, adding to the slowly changing solution the edge effect and features in the corners of the strip [5]. Substituting these solutions of the main unknowns into the formulas previously obtained after the first iteration, we obtain formulas for all the unknown unknowns of the problem of the theory of elasticity of a layered strip, valid for each point of the strip.

Petrov Y. A., Breshev E. N., Sergeev D. V. Depreciation of descent vehicles when landing on the surface of planets. Trudy MAI, 2023, no 133 The spacecraft touchdown on the surface of planets and their satellites is one of the crucial stages of the flight, since the surfaces of the planets are insufficiently studied, the kinematic parameters of the spacecraft motion may vary in a wide range.
To dampen the spacecraft touchdown, landing devices, which should ensure a touchdown with permissible overloads and a stable spacecraft position on the surface are employed.
The article considers the descent vehicles that do not have special mechanical shockabsorbing supports, and energy absorbers are installed directly on the body of the descent vehicles.
At a hard surface touchdown, such as rock outcrops, volcanic rocks, sedimentary rocks, the soil practically does not deform, and the energy of the device is being extinguished due to the energy absorbers operation. Materials with high plasticity such as foams, honeycombs, thinwalled crumpled shells, as well as inflatable shells are being employed as energy absorbers for cushioning the descent vehicle. They differ in the magnitude of the maximum relative deformation, maximum compression force, the shape of the compression diagram, and elastic recoil energy when removing the external load.
The article considers the technique for the overloads computing while spherical descent vehicles touchdown on the loose and hard ground.
This technique may be employed for the development of the descent vehicles touchdown damping on the surface of planets and their satellites, with regard to various soil models.
Telemetric data from accelerometers on the spacecraft acceleration at the impact with the surface and this impact duration, allows computing the soil bearing capacity and its density at the touchdown site by the proposed methodology.
Touchdown ensuring of the descent vehicles with permissible overloads is especially important for vehicles returned to Earth with soil. The design of the descent vehicles to confirm the calculated maximum overloads should be tested for strength during throwing tests. Besides, the capsule with the soil should remain sealed after touchdown of the descent vehicles on any soil to exclude microbiological contamination of the surface of the touchdown area. 
Lyashevskiy A. V., Prokopenko E. A., Ginzburg T. V., Golovchanskaya N. V. Study of the opening process of the transformable umbrella antenna of the repeater spacecraft taking into accout vibrations of the mechanical system. Trudy MAI, 2023, no 133 The spacecraft antenna reflector (netcanvas) deployment from the transport to the orbital position is accompanied by the appearance of oscillatory processes that preserve energy after its fixation in the working position [2, 3]. These fluctuations of the structure lead to the efficiency decrease of the system in total.
The article considers the results of numerical modeling of the opening process of a repeater spacecraft transformable umbrella antenna to analyze the kinematics and dynamics of the largesized antennas opening to assess the effectiveness of the spacecraft functioning.
A model of a transformable antenna of the “Beam” repeater spacecraft, consisting of formforming spokes fixed pivotally to the base, and a network canvas stretched between them was considered as a prototype. The kinematic scheme of the antenna structure consists of a spoke fixed pivotally to a fixed base; a connecting rod connected pivotally to a spoke and a slider and performing planeparallel motion; a slider moving translationally.
The effect of the elastic modulus of the material on the magnitude of residual vibrations and their frequency was found. The change in the design, allowing reducing the residual vibrations value was proposed and analyzed.
The simulation results analysis allowed revealing the effect of the initializing force nature and the materials employed in the design on the final velocity, final acceleration, opening time, required initialization force, voltage, amplitude of residual oscillations and their frequency, frequency and forms of natural oscillations of the spacecraft antenna structural elements.
The proposed approach to the analysis of largesized spacecraft antennas allows accounting for the effect of the materials of the spacecraft structural elements antenna and the initializing force nature on the final speed, final acceleration, opening time, required initialization force, voltage. 
Dobryshkin A. Y., Sysoev O. E., Sysoev E. O. Experimental verification of the mathematical model of free vibrations of a plate with rigidly clamped edges. Trudy MAI, 2023, no 133 The article considers the results of experimental studies on testing a new mathematical model of a thinwalled plate with rigidly clamped edges free oscillations. As of today, plate designs with rigidly fixed edges are widely employed in aircraft building and construction structures: buildings and structures, as well as in various industries. At the same time, these structures are subjected to various loads (wind, snow, and vibration), which cause free vibrations and lead to resonance phenomena, in some cases, structural failure and technogenic disasters. Experimental studies today is one of the most effective. The external forces impact on the shell allows obtaining experimental dependences of the frequency response of the shell vibrations and the value of the attached mass with the test bench. The study of plate free vibrations allows studying the resonant vibration modes, the parameters of their onset, prevent destruction of the real shell structures. Vibrations with moderate amplitudes of free oscillations were decomposed according to the obtained equations. Verification of the discrete nonlinear oscillations model of the thin shell pinched at the edges, obtained during the research, was conducted using the multiscale method. When performing experimental studies, a noncontact frequency response meter of the HSV2000 system was applied. It consists of the HSV2001/2002 controller, HSV800 laser unit and the rugged compact HSV700 sensor head. The laser unit contains the interferometer and the lowpower laser, as well as the Rohde & Schwarz RTB2002 oscilloscope. Based on the results of the research, experimental verification of the free oscillations mathematical model of a plate with rigidly clamped edges was performed. The results of the work allowed describing the dependence of the first eigenvalue λ on ε for the recursive formulation of the perturbation theory and the Padé approximation, as well as experimental data. The limiting value of the ε parameter, at which the difference in the results obtained by the recursive formulation of the perturbation theory and the Padé approximation will be within 5%, is ε = 0.4. 
Myo Z. A. Deformations of the viscoelastic layer of the Earth under the influence of the gravitational forces of the moon and sun. Trudy MAI, 2023, no 133 The presented article is studying the problem of the viscoelastic layer of the Earth deformations under the action of the forces of attraction of the Moon and the Sun through the modal approach. A viscoelastic solid consisting of an axisymmetric solid core and a viscoelastic axisymmetric (in anindeformed state) shell subject to deformation according to the Kelvin–Voigt model was considered as the Earth model. There are no displacements on the inner boundary of the shell, and the outer boundary is free. The process of the Earth deformation is assumed to be considered as quasistationary.
Based on the deformation equations derived from the DalembertLagrange variation principle, approximate expressions for the frequencies of solidstate tides are obtained in the work. A modal approach is used for this purpose. The author demonstrates that oscillations will occur only on the forms with 0, 1 and 2 indices. The frequencies of the forced tidal oscillations of the Earth mantle deformable layer are approximately determined for these forms The resulting set of harmonics includes not only the basic tidal harmonics, but the minor smallscale components with combinational frequencies as well. The results of the observation variations approximation in gravity acceleration in the city of Membach on a superconducting SGgravimeter, built using the developed tidal model are presented as an example.
The models of tidal deformations of the viscoelastic Earth are employed in the problems that require a highly accurate description of the gravitational field, such as, in the problems of the spacecraft orbital motion. Thus, the lunarsolar tides in the of satellites motion lead to quite noticeable disturbing accelerations. For example, for highorbit satellites with an orbit altitude of about 20,000 km (GLONASS, GPS), the disturbing acceleration is of the order of 2*10^{9}m/s^{2}, and for loworbit satellites with an orbit altitude of about 350400 km (ISS), the acceleration value is already much greater, namely of the order of 1.5*10^{7}m/s^{2}. For example, neglecting the perturbing acceleration of the order of 2*10^{9}m/s^{2}for GLONASS leads to a daily orbital drift of about 23 meters.
However, the issues related to the description of tides turn out to be important not only in the tasks of clarifying coordinatetime and navigation support, but in the tasks of the tidal evolution of the planets motion and their satellites in celestial mechanics and astrodynamics. 
Temnov A. N., Yan N. O. On the stability of stationary rotation of a solid body with a cavity containing a cryogenic liquid. Trudy MAI, 2023, no 133 The article considers the stationary rotation stability of a solid body with a cylindrical cavity completely filled with incompressible cryogenic liquid. The stationary rotation stability of a body with stratified liquid is being studied based on ordinary differential equations, which coefficients are being determined from the solution of timeindependent boundary value problems of hydrodynamics. A distinctive feature of all cryogenic liquids is the nonuniform change of density and temperature observed in all storage and operation modes. The most significant stratification of the cryogenic component occurs in the direction of action of the external field of mass forces. To study motions of this mechanical system, a stratified incompressible fluid is a suitable model. The authors studied various cases: (a) the case of solid body rotation in the absence of liquid mass and with solidified liquid; (b) the case of solid body rotation with homogeneous liquid, when the moment of inertia of the solid body equals to zero or not equal to zero; (c) the case of solid body rotation with stratified liquid, when the moment of inertia of the solid body equals zero or not equal to zero. Characteristic equations of the boundary value problem and the motion of a solid body with a stratified fluid stationary rotating about its axis were obtained. The stability regions of free rotation of a solid with stratified fluid in dimensionless parameters are plotted. The obtained results allow drawing inference that stable stratification of the fluid leads to a decrease in the areas of instability in the rotation of a solid body with a cylindrical cavity completely filled with fluid. The considered method maybe used for studying not only the cylindrical cavity, but the other forms of cavity as well. 
Sharunov A. V. Determination of the optimal way to increase the inner radius of a thickwalled cylindrical coupling made of shape memory alloy. Trudy MAI, 2023, no 133 One of the most promising applications of SMAin the aviation industry is the manufacture of couplings from them designed for thermomechanical connection (TMC) of pipelines. Currently, in the Sukhoi Design Bureau, an analysis of the possibility of using the above alloys in the hydraulic system of the aircraft has been carried out, zones of preferred use of SMA couplings in the airframe design have been identified (“dry zones”, “embedded zones” under composite panels). The use of coupling joints from SMA was also considered for carrying out repair work of fuel and hydraulic systems of aircraft directly in the places of basing and operation of aircraft.
As part of the work, mathematical models of SMA material were developed in the Simulia AbaQus finite element modeling software package, capable of describing the functional properties of SMA implemented during the entire life cycle of a coupling made of this material. In addition, the models have a high level of availability and can be used in solving most technical projects for the introduction of SMA elements into the design of aircraft, including when designing thermomechanical connections using couplings made of this material. Two alternative ways of increasing the internal radius of the SPF coupling are also proposed, a comparison with the currently used dorning method is carried out, and the optimal approach is identified.
The reliability of the results of the work is confirmed by the validation of the developed software modules based on the results of field tests of elementary samples based on the NiTi system and verification by known analytical solutions of model boundary value problems of SMA mechanics. 
Nikolsky A. A. Numerical solution of the inverse airfoil problem using the PGT technique. Trudy MAI, 2023, no 133 The purpose of the presented work consists in creating an effective method for the viscous inverse problem numerical solution based on a substantiated airfoil geometry corrector, PGT (Parent function Generating function Transformation) technique developed earlier and the concept of effective nonviscous circulation for the airfoil viscous flowaround. The possibility of this method application for the integral aerodynamic characteristics improving of the multimode profiles was studied additionally.
Universal model, allowing developing arbitrary profile, consisted of the functions generating the aerodynamic airfoil contour based on the universal parental function and two parameters, was developed earlier based on the PGT method for the aerodynamic design tasks. The PGT method distinctive feature is the fact that generating functions increase monotonically from 0 to 1 on the [0, 1] segment. The presented work employs this universal model for mathematical representation of the velocity circulation distribution around the airfoil contour. The model allowed solution efficiency increasing of a wellposed inverse problem for the full potential equation. The same model was employed for setting and solving the inverse problem for the profile in a viscous flow as well. Verification of the viscous inverse problem solution was performed on the example of the NACA23012 profile. The examples of the profile contour resurrection by the pressure distribution in it for several flowaround modes were presented.
The article presents demonstration example, which reveals the possibility of the multimode airfoil aerodynamic characteristics improving based on the inverse viscous problem solution.
The author shows that wellposed nonviscous inverse problem solving method application as a corrector allows realizing pressure distribution along the upper contour of the airfoil practically coinciding with the target one.
The presented study revealed that the original mathematical model based on the PGT method and application of the concept of effective nonviscous circulation allows creating an effective method for a viscous inverse problem solving and efficiency improving of the method for the wellposed nonviscous inverse problem solving. 
Basharina T. A., Glebov S. E., Akolzin I. V. Investigation of water shock wave propagation in a pistontype pressure stabilizer. Trudy MAI, 2023, no 133 In the field of hydraulics in modern mechanical engineering, the issue of wear and tear of piping systems is particularly acute, as pipelines often become unsatisfactory for operation due to internal damage caused by the constant impact of hydraulic shocks on the pipe walls. This process is widely studied, the key feature of hydrostroke is the wavelike propagation of pressure surge along the pipeline at a speed comparable to the speed of sound in the working medium. Pressure stabilizers are used to minimize the effects of hydraulic shocks in pipelines. The paper presents the results of computational experiments of hydraulic shock wave propagation in a liquid working medium in a straight pipeline and a pipeline with a pistontype pressure stabilizer installed. The analytical calculation of the main parameters of the working medium in the pressure stabilizer at the moment of hydraulic shock, such as pressure of hydraulic shock and period of oscillations of the increased pressure near the piston surfaces is given. In the course of verification of the analytical method, the relative errors of calculation of the amplitude pressure of the hydraulic shock and the velocity of propagation of the hydraulic shock in the pressure stabilizer are established, each of which is less than 5%, which corresponds to an acceptable engineering accuracy. It is determined that the use of the pistontype pressure stabilizer reduces the amplitude pressure of the hydraulic shock by more than 83%, which indicates the effectiveness of the developed design and the possibility of application in various industries. 
Novogorodtsev E. V., Koltok N. G., Karpov E. V. Computational study of reynolds number influence on the oval fixedgeometry air inlet perfomance. Trudy MAI, 2023, no 133 The purpose of this research is to study the Reynolds number value effect on the flowaround characteristics and characteristics of the isolated air intake. The object of the study is a nonregulated air intake of external air compression with ovoid inlet. The air inlet is equipped with a boundary layer control system, in the form of perforation on the shell braking and trimming surface. The air intake flowaround numerical simulation was executed based on the solution of the Reynoldsaveraged NavierStokes equations with the SST turbulence model (RANSSST approach), using unstructured computational meshes built in the flow areas outside and inside the air intake. Simulation of the air intake duct throttling was performed using the active disk method. The air intake flowaround was modeled at the Re number values ranging from Re ~ 3.8х10^{6} to Re ~ 4.2х10^{7}. The air intake throttling characteristics were obtained on all studied modes by the results of the numerical modeling. The article also presents the Mach number fields in the longitudinal vertical section of the air intake duct and the total pressure recovery coefficient (ν) fields in the duct cross section, corresponding to the engine compressor inlet. The obtained results analysis revealed a number of specifics of the air inlet throttling characteristics stipulated by the Re number value. Firstly, the value of the ν coefficient increases with an increase the Re number value at the supercritical operating modes of the air intake. The maximum increase of the ν coefficient value was of Δν ≈ 0.01. The ν coefficient value increased due to the decrease of the boundary layer thickness in the air intake duct. Secondly, the ν coefficient values change slightly with a change in the Re number one the critical operating mode of the air intake. Thirdly, in subcritical operation conditions of the air intake, the ν coefficient value decreases with an increase of the Re number value. Maximum decrease of the ν coefficient value was Δν ≈ 0.01. The decrease of the ν coefficient value is associated with the losses reduction effect weakening of the flow total pressure in the λstructure, which occurs while the boundary level control system perforation flowaround. Fourth, it was revealed that the Re number in the studied values range, did not significantly affect the air intake characteristics by the _{}¯Δδ_{о}_{} parameter. Further study of the Re number value effect on the characteristics of supersonic air intakes supposes performing numerical studies on the flowaround and characteristics of the air intakes in the layout with the fuselage of prospective civil supersonic aircraft at various Re numbers, as well as conducting tests of the air intakes models at various Re numbers. 
Win K. K. Variational approach to compiling nonlinear equations of motion for a bodytwo fluids system. Trudy MAI, 2023, no 133 The dynamics of motion of a solid body interacting with a fluid is an important field of research in mechanics and physics. Particularly interesting are cases where several immiscible liquids are present in the cavity of a solid. The introduction briefly introduces the main aspects of this topic, covering both linear and nonlinear approximations. The article is devoted to the formulation of the basic equations of nonlinear dynamics of a solid body undergoing complex motion and having a cavity filled with a twolayer ideal heavy liquid. In the formulation of the problem, consideration of quasivelocities was introduced instead of generalized velocities and the EulerLagrange equation for the motion of a rigid body was used. The article shows that using the Ostrogradsky principle, a complete set of equations of motion of a rigid body relative to quasivelocities V_{o}_{i} , ω_{i} and the motion of a twolayer liquid relative to generalized coordinates B_{j }and Q_{n} was obtained. The article is devoted to the definition of differential equations for the generalized coordinate motions of a twolayer liquid in the cavity of a solid body performing a given motion in space. In the article, the formulation of a nonlinear problem about the motions of immiscible incompressible ideal liquids that completely fill a cylindrical cavity is formulated, and velocity potentials are given for each liquid. The article shows that with the help of the variational principle, written in a form different from the traditional one, it is possible to obtain a complete set of equations of nonlinear motions of liquids, including nonlinear kinematic and dynamic conditions on the interfaces of liquids filling the cavity of a solid body that performs a given movement. 
Gumarov S. G., Getmantsev A. Y. Factor analysis of the reasons determining the error of stations of technical systems (complexes) testing ground. Trudy MAI, 2023, no 133 The article considers the features of determining the essentiality of the instrumental error effect of automatic and automated optical stations of technical systems (complexes) of the test site (testing organization) (hereinafter referred to as TSCP), as well as the error introduced by the operator of automated stations on the total error of external measurements. The methodological apparatus of applying the factor analysis methods in identifying the single factor significance for the total measurement error is recounted in detail. The article presents the analysis of various radioengineering methods for the aircraft eigen coordinates determining during flight experiments aimed at obtaining their actual flight characteristics. The importance of technical means (complexes) of test sites for independent and highprecision assessment of coordinates and speed characteristics of aircraft is demonstrated.
An approach to identifying the materiality factors that introduce errors in the measurement results of various channels of TSCP is proposed. It is demonstrated that the coordinates of stars and other astronomical objects computed with the required accuracy can be accepted as reference values. Combined application of mathematical apparatus of the probability theory, mathematical statistics, analysis of variance and factor analysis allows forming a criterion for the significant and nonessential factors selection affecting the TSCP measurements accuracy. It allows accuracy and reliability assessing of the results of the aircraft external design parameters determining by technical means and complexes of the test site. The authors proposed a methodology for solving the said problematic issues. 
Gaynutdinov R. R. The shielding efficiency study of composite material for an aircraft fuselage. Trudy MAI, 2023, no 133 Currently, composite materials are used in almost all sectors of society. Composite materials are most widely used in the development of aircraft systems, including unmanned aerial vehicles. The use of composite materials, on the one hand, improves the weight and size characteristics of objects, but on the other hand, worsens the electromagnetic ones. Thus, the trends in the use of composite materials, for example, in the construction of aircraft fuselages, are negative from the point of view of ensuring their electromagnetic compatibility. The use of composite materials worsens electromagnetic characteristics, which is due to their low and frequencydependent electrical conductivity. Due to their low electrical conductivity and anisotropy, composite materials have low shielding efficiency. The lack of proper shielding eliminates the first line of protection of onboard equipment from external electromagnetic influences and intrasystem interactions. In this work, experimental studies of the electromagnetic characteristics of a composite material sample are carried out. An experimental stand is proposed for studying the electromagnetic characteristics of a composite material. The composite material is a layered fiberglass material. The middle layer of the composite material in question is made of a plastic porous structure with embedded metal strips. The results of experimental studies of the electromagnetic characteristics of a composite material sample were obtained. The shielding efficiency of a composite material sample is quite low. In this case, the electromagnetic fields generally pass through the test sample of the composite material without noticeable attenuation. The effectiveness of sample shielding at different frequencies is uneven, which is due to the design of the composite material and resonance effects. To improve the electromagnetic characteristics of the material sample under study, it should be recommended that one of the outer layers be made using carbon fibers, which should increase the shielding efficiency without increasing the reflection coefficient. 
Volkov A. S., Solodkov A. V. Design of an integrated circuit topology for an algebraic convolutional codec. Trudy MAI, 2023, no 133 Modern telecommunication systems and communication networks development is being accompanied by a permanent growth of the transmitted messages volume and speed. High demands are placed herewith on the transmitted information reliability, both in wired and wireless systems. The problem solution to the of transmitted information reliability increasing is the errorcorrecting convolutional coding and decoding methods application. At the same time, Russian telecommunications companies are showing interest in domestic developments in microelectronics to ensure target indicators of domestic communication systems noise immunity.
The purpose of this article consists in the topology designing of an integrated circuit for codec of algebraic convolutional (n, k)code. The work was funded by the Ministry of Education and Science of Russia within the framework of Federal project “Training of personnel and scientific foundation for the electronics industry” according to the State assignment for the implementation of research work “Development of the Technique for Electronic Component Base Prototyping with Domestic Microelectronic Production based on the MPW Service (FSMR20230008)”.
The authors considered a coding algorithm, defining a convolutional code in a polynomial manner through a set of generating polynomials. This approach allows determining the convolutional code parameters at the design stage. Two decoding algorithms have been proposed: the Viterbi algorithm and the algebraic decoding algorithm.
The integrated circuit topology of the algebraic convolutional codec has been designed, and its main parameters description has been performed. These parameters are as follows: the number of chip contacts is 52; the size is 20 х 20 microns; maximum operating frequency is up to 250 MHz, and peak consumption is of no more than 200 mA.
The integrated circuit of the algebraic convolutional codec allows both algebraic decoding at the length of the code word section and Viterbi decoding applying soft decision metrics.
As the result of modeling, the following values of the E_{b}/N_{0} ratio for bit error probability of q_{bit} = 10^{–3} were obtained: 5.68 dB at R ≈ 2/3 and 6.12 dB at R ≈ 1/2 and 6.91 dB at R ≈ 1/3. The obtained values for the E_{b}/N_{0} ratio for the bit error probability q_{bit} = 10^{–6} corresponds to the following values: .23 dB at R ≈ 2/3; 8.41 dB at R ≈ 1/2 and 9.18 dB at R ≈ 1/3. 
Aliyeva A. J., Huseynova M. V., Gumbatov D. A. Issues of attenuation of the interelectronic electromagnetic impact of the warring parties. Trudy MAI, 2023, no 133 As of today, the UAVs application covers both peaceful and military spheres of human activity, which highlights various tasks of their functioning optimization and modeling. The wide prevalence and development of theory and practice of the UAV group flights has naturally led to the solution of many issues on ensuring high efficiency of data transmission in the communication networks of the UAV group. In military conflicts, the struggle of the opposing sides often leads to collateral flights of various drones, in which drones of the opposing sides participate. The drone of one of the contending sides herewith may be tasked with silencing or disabling the drones of the opposing side. The purpose of the study is to determine the conditions for neutralizing the effects of powerful radio emission emanating from a specialpurpose drone, which function consists in neutralizing drones of the other side. The authors considered a scheme, in which the second party to the conflict employs a drone carrying a powerful generator of silencing electromagnetic radiation of the same wavelength on which the drones of the first party operate to jam and neutralize the functioning of the drones of the first party. The case of radiation propagation along the lineofsight trajectory is being considered. The condition justified by the necessity of the minimum possible deviation of the attacked drone from the originally set trajectory is determined. The problem of optimal retreat from the initially set trajectory of the attacked drone due to the effects of damping electromagnetic radiation was formulated and solved. The condition of achieving minimum impact of the damping electromagnetic radiation of the second party drone on the first party drone is determined. 
Ananenko V. M. Analytical model of determination of orbital object motion parameters by results of its observations from spacecraft on the basis of neural network. Trudy MAI, 2023, no 133 The article presents the results of scientific and methodological approach to the possibility of solving the problem of motion parameters autonomous determining of noncooperated orbital object in the form of the orbit elements. This requires measuring relative flight parameters of the orbital object flyby in the area of the spacecraft. Measurements are being conducted by the spacecraft onboard optoelectronic equipment. The zenith distances of the orbital object at characteristic points of the spacecraft orbit and the orbital object flyby time between these points are selected as the measured parameters. Such characteristic points of the orbit are the locations of the spacecraft at the moments when the orbital object crosses the plane perpendicular to the plane of the spacecraft and the plane of the spacecraft orbit. The obtained information is being processed employing a multilayer feed forward neural network. The output of the neural network is used to determine directly the motion parameters of the orbital object.
The obtained results can be implemeneted in the design and research of neural networks for autonomous of the orbital object motion parameters determining based on the results of its observation from the spacecraft with optoelectronic devices. The article considered the effect of the neural network size changing in both the number of internal layers and the number of neurons in each layer on the accuracy of solving the problem of motion parameters determining of an orbital object. 
Bolshakov R. S., Gozbenko V. E., Quang T. V. Mathematical modeling of dynamic conditions of vibration machines. Trudy MAI, 2023, no 133 The subject of the study is a technical object in the form of a vibration technological machine used in the implementation of technological processes associated with vibration hardening, transportation, sorting, etc. The technical object under consideration contains massinertial and elastic elements.
The purpose of the study is to assess the possibilities of changing the dynamic condition of a vibration technological machine by adjusting the parameters of the constituent elements to obtain stable dynamic operating modes of the technological equipment in question.
As a research tool, structural mathematical modeling is used, based on the use of dynamic analogues of the original design diagrams of vibration technological machines in the form of mechanical oscillatory systems with several degrees of freedom, which are structural diagrams of automatic control systems.
The main results obtained during the research include the construction of a mathematical model of a vibration technological machine, which allows one to assess the dynamic comdition of the technical object under study, as well as change parameters to obtain motion modes in which there are no angular vibrations of the working body of the vibration technological machine.
The use of the obtained results is possible when modernizing and designing vibration technological machines by introducing additional elements into their structure, the parameters of which can vary depending on the type of technological process. Based on the proposed method, a control system for the technical object under consideration can be created.
The conducted research allows us to propose a method for assessing the dynamic interactions between the elements of a vibration technological machine. 
Baranovsky A. M., Musienko A. S., Shulika N. R. Algorithm for searching for defects such as “short circuit” in the electrical circuits of the cable network of a complex automated system. Trudy MAI, 2023, no 133 In complex automated control systems (ACS), specifically in the control systems of the spaceintended rockets (SIR) singular defects manifest themselves in the form of short circuit in the electric circuits. The authors propose a new search algorithm, which reduces the number of search steps through a combined strategy of partitioning the initial set of possible defects.
The strategy being proposed includes the principle of halfpartitioning and sequential enumeration of possible defects. It differs from the wellknown strategies, such as exhaustive search, halfpartitioning and mixed strategy, allowing not only detecting the presence of a defect, but identifying specific circuits that communicate with each other with a minimum number of checking steps as well.
The obtained research results of the study can be employed in the development of monitoring devices for electrical equipment of ground and onboard systems, which ensusre monitoring and detection of defects during the preparation of the SIR for launch. Both external and internal factors may cause changes in the technical condition of electrical circuits during operation. Defects, especially short circuits between the circuits, are especially dangerous and do not allow for he safe operation of the products.
The purpose of the study consists in reducing the number of check steps to detect the fact of the short circuit absence and indicate the circuits numbers that have a short circuit between them, in the event of a short circuit being detected in electrical circuits.
The authors propose to employ original heuristic algorithm for generating sets of tested circuits to achieve this goal. This algorithm allows generating a terminal minimum set of pairs of circuits with supposed presence of the short circuit. This approach reduces the number of necessary pairwise checks at the stage of sequential enumeration of the checked pairs of circuits.
In conclusion, the proposed strategy for the single defects searching in electrical circuits is the best one, since it requires fewer elementary tests to monitor and search for the short circuits. Such strategy realization is relatively simple with modern control tools based on computing and switching devices. The assumption of a single short circuit is acceptable for normal operating conditions, but in case of deviations a repeated round of checks is necessary. 
Belyakov A. A., Shulepov A. I., Shesteryakov S. I., Prihodko V. I., Kabushev I. S., Prokopiev E. V., Muradov A. A. Ergomonic, mounting, size requirments implementation while automatically arranging devices in compartments of rocket and space vehicles. Trudy MAI, 2023, no 133 The processes of the onboard equipment mounting involves a considerable amount of work to ensure the interchangeability of elements comprising the systems, as well as testing and finetuning their output parameters, which requires accounting for specific operating conditions, thermal, mechanical and other loads, starting from the stage of preliminary design (technical proposal).
Attention is paid herewith mainly to the masscentering or thermal characteristics of the compartment, or the electromagnetic compatibility of the onboard equipment components. This approach is typical for the stages of a technical proposal development, and preliminary product design. But further, at the stage of working design documentation development (less often at the stage of technical project), a detailed study of the design for the layout of the compartment begins, leading to an increase in the importance of ergonomic, installation, overall requirements, especially for manned space vehicles. Ergonomic, mounting and overall requirements for the devices arrangement are interconnected since all of them refer to the same installation processes of the onboard equipment and its operation from different angles.
The dependence of mounting clearances on the design of fasteners on the masses of the installed devices was obtained based on statistical data. The method for assessing the onboard equipment belonging to a particular location zone has been proposed. Assessment of the anthropometric and physiological characteristics of the operator to control the ergonomic requirements meeting the devices layout occupies the central place in the study.
Calculation formula for correcting the electronic geometric models coordinates of the onboard equipment in the event of intersections with the structure was proposed. Testing was performed on the example of one of the largesized manned spacecraft for scientific purposes. The role of electronic and material modeling was also noted to confirm the prototyping results. The software created in the course of the work is supposed to be employed in the development of design documentation at space engineering enterprises after extra updates to the algorithm. 
Bukirev A. S. Method for diagnosing an aircraft onboard equipment complex based on machine learning. Trudy MAI, 2023, no 133 The article presents an analysis of existing methods and control means employed onboard a modern aircraft. The author substantiates the necessity and possibility of increasing the depth of search for the failure location by the machine learning methods application, allowing automatically create and employ diagnostic models being difficult to formalize. A modified algorithm for the onboard equipment informationtransforming elements diagnosing of was developed. The algorithm is based on machine learning through interaction with a multiplex information exchange channel, with a modification of the algorithm in terms of using a block for automatically assigning optimal training parameters, according to the criterion of ensuring its full autonomy (training without a teacher), due to preliminary analysis of the training sample for each informationtransforming element. The article considers the problem of the external disturbing impacts effect on the result of the informationconverting elements of onboard equipment diagnosing. To compensate for these impacts, a modified Kalman filter with automatic determining of optimal filtering parameters is applied for each informationtransforming element, due to the training sample preliminary analysis. The developed algorithm combines the integration (ensembling) of the three machinelearning models, with the majority principle of generating at the output the control result of each informationtransforming element using the “two out of three” method, to increase the control results reliability, as well as minimize the likelihood of first and second errors of the second kind when diagnosing. In this work, by informationconverting elements the onboard equipment performing its functions through the multiplex information exchange channel is meant. The aircraft recovery time is expected herewith to be reduced by minimizing the time for the failure location searching, which will allow increasing the main complex indicator of the aircraft reliability, namely the availability factor. 
Kulikov G. G., Rizvanov K. A., Ivanov A. V., Shukaluk V. A. Transformation of an automated information and control system for constructing system mathematical models of gas turbine engines in the form of digital twins. Trudy MAI, 2023, no 133 The article studies the system technology application in the process of the of digital twins development for employing in the engine manufacturing industry. The authors define the basic requirements and specific features of creating digital twins, as well as consider a systemiclinguistic approach to the formal models forming of the subject area being studied. This approach allows ensuring the proper level of formalization in the process of creating digital twins of both real and virtual objects, while maintaining their causeandeffect relationships. The authors consider as well the logic of digital twins representing in the spacetime Minkowski coordinate system, with account for the cybernetic principle of their physical realizability. As an example of this methodology application, the authors present system models of metalanguages and system models of gas turbine engines (GTE), as objects of management and control, as well as a model for the GTE resources formation starting from the technical proposal stage for their development. Thus, the results of the analysis of enhancing of the systems engineering principles and methods efficiency while digital twins developing are presented. 
Dubinsky S. V., Strelkov V. V. Promising research areas aimed at building an integrated flight safety management system. Trudy MAI, 2023, no 133 Flight safety remains a priority challenge in the aviation industry. The transition to predictive technologies seems to be the most promising way to meet this challenge today. Continuous monitoring of power plant characteristics, onboard equipment, airframe structure health status and the flight crew actions during operation allows early identification of prerequisites for failures or flight incidents or accidents in order to take measures to prevent and counteract them. This paper considers some promising areas of research aimed at building an integrated flight safety management system, including a system to monitor the state of aircraft structure, the condition of power plant and the current flight situation as a whole. These researches should result in demonstrators of the proposed technical solutions and technologies discussed in this paper.
The researches of onboard systems for aircraft structure health monitoring include the three following areas:
1) monitoring of accumulated growing fatigue damage (safe operation life monitoring);
2) monitoring of structure integrity (detection of cracks, corrosion pits, etc.);
3) impact damages events monitoring (localization and impact energy recovery).
The first of the three focus areas mentioned above is the most elaborated one. Progress in the fiberoptic technology opens the prospects for fitting all aircraft by system of optic strain gauges and improving technology of accumulated fatigue damage monitoring. Online monitoring technologies of airframe integrity and impact damages localization are now at a stage of laboratory study.
At the present time, electric power supply actuators are widely used in unmanned vehicles and they have some prospect to be used in the advance “more electric” aircraft. Therefore, its health status has to be revising in operation. Monitoring technology for electromechanical actuator and its demonstrator are discussed in the paper.
One more research area for flight safety is monitoring of flight situation and prediction of its progress. The advanced runway overrun awareness and alerting system, its functionality, architecture and ground based demonstrator are discussed. 
Grigoriev E. K., Sergeev A. M. Method for security coding of data received by optical sensors of unmanned aircraft systems. Trudy MAI, 2023, no 133 At the current time, unmanned aerial systems (UAS) are widely used in solving problems of realtime monitoring, ecological exploration, inspection of protected areas, as well as in the creation of various media content. One of the main channels for obtaining information is the optical channel.
The article discusses the relevance of the problem of the confidentiality ensuring of visual information received by optical sensors of (UAS). The inference is being made that the main factor hindering the implementation of algorithms data protection received by the civil UAS optical sensors is their computational complexity. In this respect, to searching for and implementing mathematically simple protection techniques seems to be expedient. The authors propose employing matrix masking as an alternative as an alternative to the cryptographic methods for the discussed problem solution. Masking specifics of the fullcolor images and video stream frames received by the UAS payload are being considered and analyzed. The results of the analysis reveal that masking results in color images reduction to a noiselike form with complete destruction of the contours of the original image, making any visual analytical analysis impossible in the case of equal image sizes and keymatrix sizes. The authors revealed that the fullcolor images masking has its own specifics in contrast to the halftone images masking, and, as a consequence, ensure better pixels mixing and better contours destruction of the initial image compared to the halftone images masking. Masking with the smallsize key matrices thereby becomes possible. 
Zhashuev R. M., Sokolova Y. V., Sysoev V. K., Yudin A. D. Selection of parameters for the operation of a demonstration solar space power plant. Trudy MAI, 2023, no 133 The article analyzes the necessary parameters of the functioning of a demonstration solar space power plant with a laser energy transmission channel. Currently, there are also physical and technical problems that complicate the implementation of space solar power plants. This is the need for large massdimensional parameters of solar power plants for energy collection, the need to create an energy transmission channel with high efficiency and high precision guidance and ensuring the thermal operation of solar power plants at high capacities.
The authors consider the basic parameters of such power plants. The transmitted power of laser radiation from the spacecraft is in the range of 10100 kW. The diameter of the mirrors of the laser emitter is selected within 1÷5 meters. The choice of the orbit height, which is limited to the following options: geostationary orbit, sunsynchronous orbit with a height of 5001000 km and elliptical orbit of the "Lightning" type
An important condition for the transfer of energy from a demonstration solar power plant to an Earth site is the size of the laser spot and its spread. Their total value should not exceed the size of the surface of the earth's phototransformers, the accepted diameter of 100 meters. Detailed calculations were carried out for a mirror diameter of 2 meters.
When determining the design appearance of a demonstration space power plant, in terms of geometric dimensions, the area of solar panels of such a power plant was estimated, depending on the estimated power and efficiency of the photo converters.
Currently, it is very difficult to estimate the design parameters of such a spacecraft, especially the massdimensional ones, but as can be seen from previous estimates, they will be very significant. Modern space technology makes it possible to estimate such a demonstration space power plant in the range from 5 to 8 tons. 
Popov D. G., Nesterenko O. E., Romanov A. V., Trepkov R. E. The method of optimal planning of computing resources of the onboard computing complex of the spacecraft in the conditions of a difficulttopredict increase in computing load. Trudy MAI, 2023, no 133 The work is devoted to the study of the issues of the effectiveness of the functioning of the onboard computer complex of the Earth remote sensing spacecraft in the process of data collection and processing, depending on the phonotarget situation.
The issues of choosing the optimal planning of computing resources on the means of the onboard computing complex of the Earth remote sensing spacecraft in conditions of a difficulttopredict increase in computing load are considered.
In cases where it is necessary to process information about a large number of observed objects, some of them may not be identified. First of all, this is due to the imperfection of existing information processing algorithms. In some cases, the information frames received for processing have very poor image quality as a result of the influence of various disturbing factors. In this regard, it becomes necessary to use all available computing resources to process information about difficulttoidentify observable objects. With large volumes of input information, as well as when solving a variety of tasks by an onboard computing complex, computing resources can be distributed unevenly. Some of the useful information may be lost, which will lead to a decrease in the reliability of the identification of surveillance objects.
The paper describes a stepbystep method for finding optimal planning of computing resources.
Due to the optimal planning of computing resources, or the redistribution of solved tasks or subtasks between all available computing modules, it is necessary to establish the dependence of the probability of reliable detection of observed objects on the quality and intensity of incoming information for processing.
In the work, the problem is formulated and the method of searching for optimal planning of computing resources is gradually described.
To solve the problem of planning computing resources, a simulation experiment was carried out, which is implemented in the software and algorithmic complex of the functioning of the onboard computer complex of the Earth remote sensing spacecraft in the objectoriented programming language C++.
When planning computing resources, the proposed approach takes into account the dependence of processing time on the number of observed objects received in information frames with low image quality, which can reduce the loss of useful information and thereby increase the reliability of the identification of observed objects.
After choosing the optimal plan of computing resources, the loss of useful information decreased, as a result of which the percentage of identifiable objects of observation increased. 
Tanygin M. O., Chesnokova A. A., Dobritsa V. P. Organization of storage of results of intermediate calculations in tasks of authentication of message sources of limited length. Trudy MAI, 2023, no 133 The authors conducted a study on the practical implementation of the approach to the message sources of limited length authentication. This approach is based on the coding application in the blocks chaining mode. Organization of the address space for the intermediate calculations results storing, which are presented in the form of an oriented tree graph, is described. The article demonstrates the possibility of identifying sections for each such graph where its modification occurs, and the sections, which turned out to be unmodified at certain stages of the authentication procedure execution. Such a difference in access modes is a prerequisite for organizing a system of parallel processing of these graph structures.
The article demonstrates as well that application of this memory organization allows dividing the entire procedure of processing a message of limited length into five stages. Of these stages, the three can be implemented by specialized modules that operate in parallel and access the disjoint areas of the register matrix. Implementation of asynchronous parallel operation of modules, executing decoding operations of the incoming data packets, their placing in the disjoint areas of register memory and analyzing the results of intermediate calculations allows to increasing the authentication procedure speed.
An assessment of the theoretically achievable level of parallelization of the message processing procedure was performed as well. The assessment revealed that the bit depth of the authentication code determines the nature of the maximum level of parallelization dependence on the number of interacting sources. In case of the code bit depth exceeds the theoretical applicability limit of the approach based on coding in the block coupling mode, it is advisable to employ no more than five decoding and processing blocks in a treelike system for parallel operation, while dividing the memory space for storing intermediate results into an appropriate number of areas. 
Sedel'nikov A. V., Nikolaeva A. S., Serdakova V. V. Assessing the feasibility of small spacecraft angular velocity requirements taking into account temperature shock. Trudy MAI, 2023, no 132 The main purpose of the work consists in evaluating the requirements feasibility for target values ensuring of angular velocity of a small Earth remote probing spacecraft with account for the temperature shock.
The temperature shock phenomenon of solar panels occurs while a spacecraft movement from the Earth shadow to the sunlit parts of the orbit or, vice versa, when it enters the Earth shadow. In these cases, the heat flux from the Sun sharply changes, which significantly affects the bulky elastic elements (solar panels, radiators, antennas, etc.) of the spacecraft. Thus, the exit from the Earth shadow is accompanied, for example, by the heat flux origination, and dashing heating of bulky elastic elements. Heating, in its turn, leads to their temperature deformations. This factor is the cause of perturbations that affect the spacecraft motion, especially when it comes to a small spacecraft, since in this case mass ratios of bulky elastic elements to spacecraft the total mass are much higher. Thus, the studies of temperature shock for a small spacecraft are most relevant.
Analysis of a number of studies reveals that the temperature shock phenomenon leads to the accuracy decrease of a small Earth remote probing spacecraft guidance at the target object, and reduces the quality of the target task performing. In separate cases, there was even talk of possible stability loss of a spacecraft itself.
The article deals with the of temperature shock impact of solar panels within the framework of onedimensional heat conduction model. A thin plate is being used as a first approximation model of solar panels. A 1D thermoelasticity problem has been set to study the stressstrain state of the plate. This problem solution is the of the plate middle layer deflection occurring due to temperature shock.
The dependences of perturbing factors on the temperature shock were obtained in this work. The motion parameters of a small spacecraft resulting from these perturbations were estimated.
Numerical modeling was performed with the Wolfram Mathematica for the EO1 small Earth remote probing spacecraft.
As the result of the research, the values of angular velocity of the EO1 small spacecraft were evaluated and the feasibility of angular velocity requirements for modern small Earth remote probinng spacecraft was analyzed. The results of the work may be employed in performing Earth remote probing tasks by small spacecraft. 
Popov I. P. Multidimensional planar monojet oscillations. Trudy MAI, 2023, no 132 The relevance of the study is determined by the fact that fluctuations of inertial masses are found everywhere. In the field of construction and use of aviation and rocket technology, this topic is of particular importance. Like a threedimensional plane coordinate system in the coordinate plane Z, a multidimensional system with n axes 0x_{z1}, 0x_{z2},...,_{ }0x_{zn}_{ }shifted relative to each other by angles 2π/n can be considered. There is an arbitrary vector R emanating from the origin 0. R ⊂ Z . It is proved that the points x_{1},x_{2},...,x_{n}, which are the coordinates of the end of the vector R in the coordinate system 0x_{z1}, 0x_{z2},...,_{ }0x_{zn}, are the vertices of a regular polygon. The shape and dimensions of the polygon are not related to the coordinates of the vector R, i.e. are unchanged. The center of a regular polygon in all cases coincides with the middle of the vector R . In the considered (idealized) case, the polygon, at the vertices of which there are oscillating weights of masses m, lies in the Z plane. multipiston mechanism). In the considered multidimensional plane monoreactive oscillator, free harmonic linear oscillations of loads can occur. In this case, only kinetic energy is involved in the energy exchange. There is no need for elastic elements. The oscillator does not have a fixed natural oscillation frequency. The frequency depends on the initial speeds and positions of the weights. A regular polygon x_{1},x_{2},...,x_{n} makes a double rotation – around the point 0 and around the point r. At the same time, the loads carry out linear harmonic oscillations with amplitude R. The use of a crankslider or crankandrod mechanism will allow organizing the parallel movement of goods. 
Grishakin V. T. Identification of forces in the supports of multispan beams. Trudy MAI, 2023, no 132 The article considers transverse vibrations of conservative mechanical systems in the form of hinged beams of the refined S.P. Timoshenko theory with deformable intermediate supports. Deformation processes in beams resulted through the concentrated inertial forces application moving at a constant speed. Solution of the direct problem (the problem of determining parameters of the stressstrain state of a beam from a given value of the moving force) was obtained in the form of expansion in Fourier series, followed by the application of operational calculus. The inverse problem of the deformable solid body mechanics, which consisted in identifying the forces in the supports according to the given deflections under the moving force, was considered on the example of the mechanical system under study as well. As long as the inverse problem posed in this way relates to the illposed ones (an insignificant change in the initial data corresponds to an arbitrarily large change in the calculation results), A.N. Tikhonov’s regularizing algorithm was applied to obtain a stable solution. A technique for the regularization parameter α computing is presented. Both the results of the beam deflections computing at the point of the moving force application and the results of identifying the forces in the supports of a sixspan continuous beam structure, obtained with the same stiffness values of all five elastic supports, and with a change in the stiffness of one of them (the second one) are presented. Such numerical experiment was performed to illustrate the possibility of employing the proposed method, which opens up as a result of the proposed technique application, for example, in construction practice to identify defects in the supports of structures that perceive moving loads without stopping movement along them. All relevant information on the state of structures can be obtained employing a vehicle equipped with the necessary sensors. For the said two computational cases, the time dependences of the forces in the supports, obtained both as the result of solving direct and inverse problems, are presented in the form of graphs of the corresponding functions. For the considered cases of the structure loading, the results of the largest displacements computing in the most loaded span of the beam and the maximum elastic forces arising in the most loaded support are presented as well. 
Feoktistov S. I., Andrianov I. K., Mar’in S. B. Numerical and analytical model of the stressstrain state during the expansion of thinwalled pipe blanks in a curved axisymmetric matrix. Trudy MAI, 2023, no 132 The study considers numerical and analytical modeling of the stressstrain state and force characteristics during expansion of the thinwalled pipe blanks in a curved axisymmetric matrix. The equilibrium equations of the momentless theory of thin axisymmetric shells with regard to the nonlinear plasticity, changes in wall thickness and contact friction are employed when developing the model. The computations are based on the numerical method of variable elasticity parameters, which allows determining stresses and strains; the thickness distribution in the meridian section; the amount of contact pressure, as well as to plot the change in the force distribution depending on the application point displacement of the force relative to the matrix. A mathematical model for the stressstrain state of pipe blanks estimating during expansion is developed for a matrix, which profile is described by an arbitrary function. The numerical technique for the stressstrain state computing is based on the variable elasticity parameters method, which allows solving the problem of expansion in an elasticplastic formulation. Besides, the developed model accounts for the material compressibility during elastic strain. Based on the numerical computing results, the distribution of meridian and circumferential stresses and logarithmic strains, as well as the of logarithmic strains distribution over the workpiece wall thickness are presented. An assessment of the contact pressure during crimping is performed, a decrease in the relative thickness of the workpiece along the length during distribution is noted herewith. The iterative computation process convergence by the of variable elasticity parameters method was estimated by the position of stress intensities and logarithmic strain intensities relative to the deformation diagram of the material. The proposed problem solution of the pipe blanks expansion may find application in the field of aircraft engineering in the development of thinwalled shell structures for aviation purposes. 
Bogachev V. A., Markachev N. A., Petrov Y. A., Roshchin M. N., Sergeev D. V., Shtokal A. O. Wearresistant and antifriction materials and coatings used in friction units of spacecraft structural elements manufactured by Lavochkin association. Trudy MAI, 2023, no 132 Specialized wearresistant antifriction materials and coatings are applied in space technology in friction nodes, which can work in open space and (or) atmospheric conditions of the planets under study. All antifriction and wearresistant materials and coatings can be conditionally divided into liquid lubricants (oils), greases (pastes), antifriction solid lubricants and selflubricating (antifriction) materials. Greases are soft ointments of dense thick consistency and are intended to reduce the friction force in mechanical assemblies, decrease the rubbing pairs wear, prevent tearing and jamming, and ensure the necessary service life of the friction unit. In the products developed by S.A. Lavochkin NPO, four brands of antifriction lubricants are most often used: TSIATIM221, VNII NP220, VNII NP274, VNII NP284. They have been widely tested on the Luna, Venus, Mars, Forecast and Cosmos spacecraft series. When the pressure is reduced to 0.1–10 Pa, the lubricants performance is significantly reduced. The solid lubricating coatings application allows successfully solving the problem of friction and wear reduction of open friction units. These coatings represent a mixture of powdered lubricants dispersed in binder (filmforming) polymer materials and diluted with solvents to the required viscosity for spraying them on the friction surface with subsequent heat treatment. The following solid lubricating coatings are employed in the products of NPO Lavochkina JSC: VNII NP212, VNII NP213, VNII NP230, VNII NP512, EONITE3, in which the filler is molybdenum disulfide, or a mixture of molybdenum disulfide with graphite. As an alternative to the NP512 Research Institute, MODENGY1001 and MODENGY1002 TSPS have been introduced. A significant limitation on the application of molybdenum disulfide coatings consists in the fact that at temperatures above +400°C, MoS2 begins oxidizing intensively. When molybdenum disulfide is oxidized, molybdenum trioxide is formed, which lubricating properties change to the abrasive ones, which does not allow them to be employed in the atmospheres of the planets of the Solar System, primarily Venus. In this regard, the task arises of selecting materials (friction pairs) of friction units of spacecraft that descend in the atmosphere, land and work on the surface of Venus, which can function at temperatures above +450°C, which can be achieved only through the use of selflubricating antifriction materials. New promising selflubricating antifriction materials are proposed: carboncarbon containing composite materials, partially stabilized zirconium, zirconium 702 coated with microarc oxidation. As response materials (counter body), it is proposed to consider the most common structural metal materials of spacecraft: 40X13, 30XGSA steels, aluminum alloy AMg6, titanium alloy VT6. Their laboratory testing and tribological tests are required to confirm the feasibility and feasibility of their use for friction units operating in open space and (or) the atmosphere of Venus. 
Pronina P. F. Investigation of radiation dose effect on physical and mechanical characteristics of metalized polyimide films of screenvacuum heat insulation elements. Trudy MAI, 2023, no 132 External heat transfer regulation is one of the fundamental tasks for a spacecraft operation. Thermooptical coatings and EVTIs are being related to the external heat exchange control. A typical conventional EVTI coating consists of 10120 metallized polymer films separated by glass fibers (glass voile) or polyester meshes. EVTI is the best thermal insulation material for vacuum applications and is the preferred insulation material for both spacecraft and cryogenic systems. However, traditional EVTI displays a number of disadvantages, such as its difficulty or impossibility to maintain the required value of the gap between the film layers; the difficulty of ensuring stable performance characteristics; complex manufacturing and installation process. EVTI may be subjected herewith to the mechanical impacts not only while installation, but during operation as well. All this may lead to the changes in the tacking screens density, resulting in unstable thermophysical characteristics. The work deals with the istudy of the radiation dose impact on physical and mechanical characteristics of polyimide films with metallized coating of screenvacuum (EVTI) thermal insulation elements. The tensile test of rectangular samples produced by SPE Polyplen of PM1EUOA grade with aluminum coating was performed. Preliminary part of samples was subjected to radiation equal to 25 kGy, 50 kGy. In the course of the study the following diagrams were obtained: the stressstrain diagram determined at tensile tests of the sample, and displacementloading of the sample. The level of radiation effect on each studied parameter was determined. 
Sazanov V. P., Pavlov V. F., Pismarov A. V., Matveeva K. F. Influence of the ratio of the components of the initial deformations on the distribution of the residual stresses in the strengthened layer of the part. Trudy MAI, 2023, no 132 The article presents the results of studies nce of the of initial deformations anisotropy effect on the axial, circumferential and radial distribution components of residual stresses in the hardened layer of cylindrical samples, depending on the type of surface hardening. Parameters in the hardened layer of cylindrical samples from the steel 45 after hydraulic shot blasting were assumed as the basic option for computations. The ratios between the components of the initial strains were being accepted depending on the types of surface hardening. Their ratios were being considered at chemicalthermal treatment (CTT), hydraulic shot blasting (HSB), and roller running (RR). Computations were performed on finite element models of smooth cylindrical samples with diameters of D = 10 mm and D = 25 mm. The initial deformations distributions over the hardened layer thickness are assumed to vary according to a linear law (the maximum value on the surface and the zero one at the maximum hardening depth). The necessary for the studies volume of computations was performed in the environment of the PATRAN/NASTRAN software package. Cylindrical samples modeling was performed in an axisymmetric formulation of the problem with the initial deformations replacement by the respective temperature fields. The results of the tests revealed that with all types of hardening radial stresses had positive values over the hardened layer thickness. Both radial and axial components of the initial deformations do not affect significantly herewith the residual stresses over the hardened layer thickness. Hence, the components ratio of the initial deformations does not as well play a significant role in assessing the effect of the residual stressstrain state on the endurance limit of hardened parts, which is determined, for example, by the mean integral residual stresses criterion. 
Basharina T. A., Shmatov D. P., Glebov S. E., Akolzin I. V. Investigation of jetcentrifugal nozzle of sprinkler system by computational experiment with consideration of mathematical model of medium dispersibility. Trudy MAI, 2023, no 132 Sprinkler systems of nuclear power plants (NPP) are one of the key mechanisms for eliminating the consequences of design basis accidents, which stipulates high requirements for the development of nozzles as parts of sprinkler systems. The article presents the results of computational experiment of sprinkler nozzle functioning in the continuous medium formulation, employing Continuous medium morphology and Dispersed medium morphology. Average sizes of dispersed particles were determined for the computational experiment in the formulation with regard to the medium dispersity. The basic parameter of the sprinkler nozzle, namely the angle of the torch atomization, was determined on the experiment in the wide range of the flow characteristic. The computational experiment results validation and research tests of the sprinkler nozzle was performed, which results revealed the high degree of uncertainty in the continuous medium formulation, with relative error reaching up to 25%, and high degree of certainty with the dispersive medium formulation with relative error less that 3% in each experimental point. The above said is indicative of the possibility of cost reduction on the sprinkler system and test rig development by natural tests replacing with the computational experiment. 
Temnov A. N., Yan N. O. Oscillations of a stratified rotating fluid in the field of centrifugal forces of inertia. Trudy MAI, 2023, no 132 In this paper, free oscillations of an ideal stratified incompressible fluid in a rotating cylindrical vessel are considered under the assumption that the equilibrium motion of the fluid is the rotation of a solid body. The problem of oscillations of an ideal incompressible rotating stratified fluid in the field of centrifugal inertia forces is studied. Rotating fluids are not only of scientific interest, but are also important in nature and technical applications. In technical applications, rotating liquids are found in centrifuges, in the hollow shafts of liquidcooled turbines, in stabilization of rocket rotation, in zonemelting processes of single crystal growth. Recently, there has been interest in studying the oscillations of a stratified fluid filling a vessel of finite dimensions used in various fields. In this paper, we focus our attention on the consideration of some issues related to the problems of oscillations in a stratified fluid. Some results obtained by us in the study of the problem of natural oscillations of an inhomogeneous rapidly rotating fluid that partially fills a cylindrical cavity and completely fills a coaxial cylindrical cavity of a solid body are presented. The eigenfunctions of a fluid and the eigenvalues of free oscillations of a stratified fluid filling a cylindrical cavity of a solid rapidly rotating around its vertical axis of symmetry are obtained. For sufficiently large values of the angular velocity of motion of a solid body with a liquid, the case under consideration is equivalent to the case of rotation in conditions of complete weightlessness. Numerical calculations of the eigenvalues of normal fluid oscillations at a constant buoyancy frequency are presented in the form of tables and graphs with boundary conditions for internal and surface waves. 
Baklanov A. V., Vasilevich A. A., Chechnev R. A. Investigation of the influence of magnetic fields on the degree of cleaning coked nozzles. Trudy MAI, 2023, no 132 Carbon deposition in the injectors fuel channels may occur in the gas turbine engine combustion chambers, which depends on both chemical and fraction content of the fuel. Operation of the combustion chamber with injectors subjected to carbon deposition leads to combustion processes changing in the flame tube, which in its turn may lead to the combustion chamber failure. Thus, technology development, which would allow performing the channels cleaning from the depositing products is uptodate.
Up to date, diethylene glycol, sulphur trioxide and other solvents are being applied to remove hydrocarbons with strong inclination to carbonization. Ways for hydrocarbon fuels stability enhancing are being employed as well. Hydraulic cleaning is considered to be the most advanced method.
The article adduces the results of the study on the magnetic fields impact on the degree of fuel injector channels cleaning off fuel decomposition products. It describes the fuel injector design and provides he scheme of installation employed for the injector studies. Ьodes and parameters for conducting experiments are listed.
At the first stage, the initial flow characteristic of all four injectors was measured at fuel pressures range from 0 to 3 MPa by ten points. Then the injector flushing was performed by feeding electromagnet with AC (V = 28V, I = 1.9 A) for ten hours. The injector flow characteristic was measured after each hour of operating time. 
Win K. K. Equations for generalized coordinates of nonlinear motions interface surfaces of liquids. Trudy MAI, 2023, no 132 Nonlinear problems of the dynamics of a rigid body with a cavity filled with several fluids are of considerable applied and theoretical interest. The article shows that with the help of the variational principle, written in a form different from the traditional one, it is possible to obtain a complete set of equations of nonlinear motions of liquids, including nonlinear kinematic and dynamic conditions on the interfaces of liquids filling the cavity of a solid body that performs a given movement. The variational formulation of the problem of dynamics has certain advantages, for example, from the point of view of substantiating the necessity and sufficiency of the derived equations and boundary conditions, and considering the body and fluid as one system allows one to achieve a certain multiplicity.
The article is devoted to the definition of differential equations for the generalized coordinate motions of a twolayer liquid in the cavity of a solid body performing a given motion in space. In the article, the formulation of a nonlinear problem about the motions of immiscible incompressible ideal liquids that completely fill a cylindrical cavity is formulated, and velocity potentials are given for each liquid. When obtaining differential equations for generalized coordinates of nonlinear movements of liquid interface surfaces, the variational principle of Hamilton – Ostrogradsky is used, in which a modified Lagrange function is used. As a result, infinite systems of nonlinear differential equations were obtained for the generalized coordinates of the problem under consideration in the complex motion of a rigid body, as well as differential equations in particular cases. 
Korobkov M. A., Zajkin V. D. Maskassisted radiation equalization method in the liquid crystal matrix direct exposure system. Trudy MAI, 2023, no 132 The paper investigates the possibility of using liquid crystal displays as photomasks for transferring a conductive pattern to a photosensitive material using ultraviolet light in the manufacturing processes of printed circuit boards. The work is devoted to solving the problem of nonuniformity of ultraviolet radiation in the laboratory prototype of the direct exposure machine based on the liquid crystal matrix in the production of printed circuit boards to improve the reliability of the exposure operation.
The method of equalization of radiation by using a compensating mask is proposed. It involves overlaying an additional image with different transparency rates on the pattern displayed by the liquid crystal matrix. Transparency of the mask should be selected in such a way that after exposure in each point of the working field the shade of the photoresist color is the same and coincides with the lightest part of it.
In the work, an algorithm for creating a compensating mask by evaluating the color change of photoresist was formalized and an experimental study was carried out, which confirmed the effectiveness of the proposed method. The analysis of the histograms of the brightness of the green component of the images obtained with and without the application of the masking template showed a 51% reduction in the standard deviation. Thus, the considered method allowed us to significantly reduce the problem of nonuniformity of ultraviolet radiation distribution in the prototype of the direct exposure unit, which made it possible to increase the reliability of the technological operation of exposure using the developed unit.

Ovakimyan D. N., Zelenskiy V. A., Kapalin M. V., Yereskin I. S. Research of methods and development of algorithms for integration of navigation information. Trudy MAI, 2023, no 132 The issues of improving the accuracy and reliability of navigation information by combining signals received from different sources are considered. It is proposed to solve the problem using a modified Kalman filter selected as a result of a comparative analysis of known implementations in terms of accuracy and computational complexity. The software implementation of the algorithm is performed in the MAVROS environment. One of the most important tasks of the flight controller of an unmanned aerial vehicle is to evaluate the state vector. In general, this vector is multidimensional. The aim of the work is to select a method and develop an algorithm for determining the state vector by combining navigation information. The solution of the problem of aggregation of data obtained from independent sources is provided, as a rule, by nonlinear Kalman filtering. The classical algorithm is the extended Kalman filter EKF (extended Kalman filter), which is based on the linearization of the right part of the stochastic model to estimate the mathematical expectation of an unknown state vector and covariance matrix. EKF is one of the very first algorithms proposed for solving such problems. To date, there are more modern Kalman filters – sigmapoint UKF (Unscented Kalman Filter), invariant extended IEKF (invariant extended Kalman filter), quadrature QKF. In this study, Nvidia Jetson Xavier NX was used as a hardware platform, which allows the use of resourceintensive algorithms for integrating navigation information. The use of special computing modules makes it possible to unload the flight controller and makes it relevant to study the effectiveness of modern Kalman filtering algorithms. 
Gumarov S. G., Getmantsev A. Y. Control of serviceability of technical systems (complexes) of polygons by error distribution centers. Trudy MAI, 2023, no 132 The article deals with the problems of the serviceability determining of radio–electronic stations of technical systems (complexes) of the test site (testing organization) (hereinafter – TSKP). An example of the normalized accuracy characteristics determining of optical stations of external vector measurements based on highprecision data on the of astronomical position bodies is being considered. The authors proposed a methodology for solving the identified problems, consistin in determining the discrepancies, applying a method for combining various general aggregates of the obtained results of highprecision measurements, based on a comparison of the distribution centers of general aggregates for each measuring channel. The normal law of the of residuals distribution between different general aggregates assumption is applied. The article presents a mathematical apparatus applied to determine the reliability of the obtained results. The assumption is being made on the presence of expressed and significant factors affecting the error of each of the measurement channels. Attention is being drawn to the periodic certification importance for making an informed decision on the possibility of reliable and highprecision external measurements at the test site. With the degree of informativity and automation of control increase, technical means (complexes) of the test site become highly intelligent robotic measuring means, which serviceability and operability control is being performed both in the course of their current activities (continuous monitoring) and during special verification measures such as periodic scheduled certification of measuring instruments. References to the State Standards, methodological recommendations and the main literature on the subject under consideration are adduced. 
Borshchev Y. P., Kamyshanov I. V., Sysoev V. K. Dependence of the radio technical characteristics of waveguides included in the antennafeeder systems of spacecraft and manufactured using selective laser fusion on the roughness of the channel surfaces. Trudy MAI, 2023, no 132 The article deals with the analysis of the of the radio technical characteristics dependence of waveguides as a part of the spacecraft antennafeeder systems, and manufactured by selective laser fusion, on the roughness of the channels conductive surfaces. The need for this work arose as the result of the additive technology (SLM) introduction, which opened the possibility for manufacturing new, complexprofile structures of the spacecraft antennafeeder systems elements with geometry and radio technical characteristics (RTC) close to the computed ones. However, along with numerous advantages, the SLM technology has a significant drawback, namely, the increased surface roughness (Ra) of approximately from 6.2 to 20.0 microns. At the same time, the tolerances recommended in the regulatory and reference literature for the of the conductive surfaces roughness of microwave devices are significantly lower.
The article presents the main factors of the SLM process affecting the amount of roughness, as well as the developed scheme of studies to assess the effect of roughness on the RTX of waveguides.
According to the research program, angular waveguides with channel sizes from 8,6×4,3 to 35×15 mm and transition from 8,6×4,3 to 10,7×4,3 mm, as well as straight waveguides with channel sizes of 28.5×12.6 mm were manufactured applying SLS technology, from domestic aluminum alloy powder, the channels surfaces herewith were not processed.
Straight waveguides, were arranged while 3D printing in groups at different angles relative to the construction platform.
Further, measurements of the RTX of the manufactured waveguides were performed, comparative diagrams of the frequency dependence in comparison with waveguides manufactured using traditional technology were adduced. The results of the RTX measurements revealed, in total, satisfactory results that meet the requirements of the design documentation. The results of the roughness measurements of the waveguide channels surfaces are presented.
Based on the waveguides data on roughness and the RTX, summarized in tables, the analysis of the roughness impact on the RTX was performed.
The analysis revealed that the waveguides RTX was deteriorates with an increase in the average roughness of the channel, which depends on the position of the part on the construction platform during 3Dprinting. Optimal is the position, at which the overhanging surfaces of the channels have the smallest area.
The results of the conducted studies give grounds to recommend the SLM technology application in the AFS KA waveguides manufacturing in the centimeter range without additional treatment of channel surfaces. It is necessary herewith to set rational modes of the SLM process. 
Aliyeva G. V. Optimization of observation conditions of civil aircrafts in the infrared thermal band. Trudy MAI, 2023, no 132 The article deals with the issues of observation optimizing of civilian aircraft during cruise flight employing groundbased infrared recording equipment. Allinall, the aircraft infrared spectral characteristics are the basis for its detection inflight. The main heat emitters of aircraft are the aircraft skin, heated while flight due to aerodynamic heating, as well as its engine and exhaust gases. Analysis of the ground observation possibility of civil aircraft in the daytime allows drawing the following inferences:
1. The flight speed increases monotonously up to the beginning of the descent stage.
2. The cruise flight altitude is almost unchanged.
3. The exhaust gases radiation is strongly attenuated by the atmosphere.
4. The emitted radiation during the cruise flight depends on the ambient temperature (air).
It was determined that the range of 2–4 μm was expedient for the ground observation and tracking of civil aircraft performing flight at daytime, where the basic component of the emitted radiation was the fact of the skin heating.
The author studied the issue of optimal dependence of the flight speed on the air temperature. The problem of the optimal relationship determining between the aircraft flight speed and the air temperature at which the skin temperature of a civilian vessel would reach an extreme value was formulated. The problem of unconditional variation optimization was formulated to determine optimal form of the said problem, and mathematical solution of this problem was adduced. The article demonstrates that if the civil aircraft flight should be unnoticed to heat detectors of the ground observation and tracking system, the flight should be perpetrated with the cruise speed inversely proportional to the air temperature value. Conversely, if reliable operation of the groundbased thermal detectors is required, then the above said regularity should be maximally avoided. Presumably, the first case refers to the situation when the aircraft and registering equipment belong to the conflicting sides, while the other case means that both the aircraft and heat detectors belong to the same owner. 
Koshkarov A. S., Guliy D. D., Baryaksheva V. P. Multirotor unmanned aerial vehicle emergency landing algorithm based on underlying surface image analysis. Trudy MAI, 2023, no 132 The imminent expansion of application areas of hightech products has also affected the field of unmanned aircraft systems. The use of unmanned aerial vehicles is finding increasing application in various sectors of the national economy, aviation, automotive, and the use of lightweight light unmanned aerial vehicles already covers up to 100 different sectors of the modern economy. The trend towards the use of unmanned aerial vehicles remains stable and is presumed to continue to grow in the digital economy. However, despite all the benefits, the use of drones also carries certain risks associated with the possibility of an accident that could result in the loss of the drone or damage to the environment.
Implementing emergency standards and regulations is an important aspect of unmanned aerial vehicles to ensure the safety of people, the environment, and property. In the case of multirotors, this critical capability takes the form of forced landing site selection. Common examples of events requiring an emergency landing are low battery, loss of ground contact, and deterioration in performance of satellite navigation systems. Since these emergency situations require an immediate landing, it is important to be able to have safe landing in a dense urban environment and complex transportation infrastructure. Therefore, the realization of emergency landing of a multirotor type unmanned aerial vehicle is an actual research area in the field of unmanned aviation. The use of analysis of underlying surface combined with machine learning methods and neural networks, will can significantly improve the efficiency of emergency landing methods, providing a more accurate assessment of the surface condition.
The paper presents the procedure for developing an algorithm for emergency landing of a multirotor unmanned aerial vehicle based on the analysis of the underlying surface image. The realization of the algorithm is carried out in two stages: image segmentation using the UNetFormer neural network and detection of a safe landing zone with the allocation of safe classes of objects observed in the frame, calculation of the occupied area of the unmanned aerial vehicle on the emergency frame and the range to the emergency landing zone selected by the algorithm. 
Burenko E. A. Mathematical model control loop guidance system of radio beam riding. Trudy MAI, 2023, no 132 The purpose of this article is to review the theoretical principles and practical methods for constructing a mathematical model of the control loop of a radio beam riding guidance system using modern computer simulation programs Mathcad and MATLAB – Simulink. The principles of constructing mathematical models of the control loop for a radio beam riding guidance system of a guided missile when aiming at a target by the method of combination (target covering) using modern computer simulation programs Mathcad and MATLAB – Simulink are considered. The construction of a model in the Mathcad environment using the method of numerical solution of a system of differential equations describing the control loop (modeling as a solution to the Cauchy problem), as well as the construction of a simulation model in the MATLAB environment – Simulink based on the mathematical apparatus of functional links, is considered. The modeling of the processes of missile guidance to an air target performing a maneuver with a given normal overload has been carried out. The trajectory of the control point, missile and target, obtained as a result of modeling, as well as the main phase variables of the model characterizing the process of aiming the missile at the target, are presented. The capabilities of the corresponding computer programs in modeling guidance systems are shown. The practical value of the work also lies in the possibility of using the developed mathematical models in the educational process for students to master the principles of construction and operation of guidance systems, as well as to develop the skills of mathematical modeling of the corresponding systems. 
Mitrofanova Y. A., Zagitov R. A., Trusov P. V. The influence evaluation of taking into account the conjugate heat transfer between combustion chamber parts and between the reacting flow on the results of modeling nitrogen oxides. Trudy MAI, 2023, no 132 This article is devoted to testing the applicability of the hypothesis about the influence insignificance of the conjugate heat transfer between the reacting flow and the solid walls of the flame tube and gas collector on the calculated level of nitrogen oxide emissions. Because of this hypothesis, it is possible to significantly reduce the calculation time by reducing the number of elements of the computational mesh and simplifying the mathematical model. The object of the study is a singlephase multicomponent reacting flow of a fuelair mixture. To describe the turbulent flow of the airfuel mixture in the combustion chamber of a gas turbine, the Favre averaging approach of the NavierStokes equations was used. The SST turbulence model was used to close the resulting system. The system of equations was solved numerically using the control volume method. A combined EDM/FRC combustion model was used to find the rate of the mixture components formation. The turbulence model used in this work is hybrid, it is applicable for the parameter y plus ~ 1. To achieve this condition, three variants of computational grids were constructed with different numbers of prismatic layers at a constant growth rate of cell sizes. The results of threedimensional calculations showed that the effect of the absence of conjugate heat transfer on the calculated level of nitrogen oxide emissions did not exceed 10% in the most heatloaded operating mode of the gas turbine. The total heat flow through the walls of the flame tube and gas collector did not exceed 0.5% of the total amount of heat released during fuel combustion. Thus, conclusions were made about the applicability of the hypothesis under consideration. The results of the work can be important for CFD – engineers and designers working in the combustion chamber department. 
Osipov N. A., Musienko A. S., Merkushev O. A. Reducing the volume of the test sample of spacecraft elements during control tests. Trudy MAI, 2023, no 132 The article describes a methodology, which combines a priori (additional) information and current control data of tests of elements of space vehicles in order to achieve the goals of selection and obtain a higher assessment of the object being pursued.
Proposed the technique is based on the mathematical apparatus of dynamic Bayesian networks, as well as the basic concepts and relationships of the theory of reliability and technical diagnostics of systems. The initial data is information on the technical condition of the elements of space vehicles during the test control, information on the reliability (structural and logical diagrams, failure rates of elements) of technological equipment, as well as diagnostic models linking the types of technical conditions and diagnostic signs of defective products.
It is proposed to use the selection method in a dynamic Bayesian network to identify discrepancies between products and equipment in the process of monitoring and diagnosing the technical condition of the elements of technological equipment and describing the dynamics of the process.
A posteriori inference allows you to combine heterogeneous initial information and incoming new data to obtain a comprehensive assessment during the process and the state of the process equipment in order to make an informed decision by the specialist to continue or suspend the process, if a defect is detected and take measures to eliminate them .
The advantage of this technique is the ability to take into account heterogeneous a priori information, including the format representation of the subject, and the results of control tests.
The implementation of this approach to control studies of a sample of a limited size is given. The possibility is substantiated of the possibility, based on the results of selective inspection tests, to estimate the predicted value of defective products in the entire batch with a sufficient goal for making a decision on selective control.
The method under consideration combines a priori information and data obtained as a result of tests, which, in the course of comparison, makes it possible to obtain the necessary accuracy to detect product defects.
The proposed method can be used by specialists when carrying out control and system testing operations in order to increase the efficiency of selection and detection of defective products. 
Minakov E. P., Aleksandrov M. A., Danilyuk B. A., Verbin A. V. . Trudy MAI, 2023, no 132 The article considers discrete Markov model for efficiency estimating of orbital aids for safety zones monitoring of critically significant spacecraft by the probability of dangerous objects detecting indicators and mathematical expectation of the event occurrence number, associated with the use of resourcesща the orbital monitoring aids. The author adduces mathematical estimation models of the specified random events and definitions of the optimal and required values of transition probabilities, as well as examples of the said characteristics estimation and results of numerical experiments on each of the models being suggested. Practical meaningfulness of the obtained results consists the software developing, tryingout of mathematical models and software during numerical experiments, esteems obtaining of the orbital monitoring aids application effects and their correctness evaluation, as well as proposals on their employing for technical characteristics assessment and ways of the created orbital monitoring systems application. 
Pavlov A. N., Gordeev A. V., Vorotyagin V. N. A method of operational assessment of survivability of multimode complex objects. Trudy MAI, 2023, no 132 One of the urgent tasks of the structurally complex objects studying with their multimode functioning is the task of reliability and survivability indicators assessing with regard to the structural and functional specifics of modes implementation. The article demonstrates that the problem of the survivability index estimating for monotonous structurally complex objects by iterating through the functional states of the system and variants of destructive impacts refers to the supercomplex combinatorial problems. This requires searching for the ways for the exhaustive search avoidance, including the one through the object operability polynomial application, which stores various topological properties of the structural and functional interaction of the system elements in the functioning modes implementation. Integral indicators of structural and functional reliability, as well as a formula for the operational approximate computing of structural and functional survivability values were introduced employing applying direct and dual parametric genome of the multimode object structure. The article considers the motion control system of a small spacecraft as a multimode complex object. Computations were performed and presented with an unknown cyclogram of the orientation modes implementation, and under conditions of spatial destructive impacts of the ith multiplicity. In other words, by the result of one destructive impact, i failed elements, are observed simultaneously in the system; calculations of approximate values of structural and functional survivability indicators for various extreme conditions for the use of spacecraft orientation modes. Indicators of structural and functional reliability and survivability of multimode objects are proposed, which will allow analyzing and evaluating the properties of reliability and survivability of a particular configuration option during system degradation.

Ermakov P. G., Evdokimenkov V. N., Gogolev A. A. Determination of the inclination angle of unprepared landing pad of unmanned aerial vehicle helicopter with a digital elevation map information. Trudy MAI, 2023, no 132 In the process of the target mission an emergency may occur on the helicopter type unmanned aerial vehicle (UAV) board. So, the problem of an emergency landing of the helicopter type UAV on an unprepared landing pad arises. One of the requirements for an unprepared landing pad is the requirement for a limit value of the inclination angle of a landing pad. The inclination angle of an unprepared landing pad should be no more than 10 based on this requirement. This article describes the problem of a determination of the inclination angle of an unprepared landing pad of the helicopter type UAV with a priori digital elevation map information (DEM). A DEM has such information as: geographic latitude and longitude coordinates of the Earth’s surface point, a height of the point of interest and a type of the Earth’s surface point. Also, a DEM contains random errors, so a determination of the inclination angle is a statistical problem. The description of the developed technique and the proposed optimal algorithm of a determination of the inclination angle with a priori digital elevation map is given. To test the performance of the developed technique of a determination of the inclination angle with a DEM the special software is constructed. The results of a simulation modelling of the proposed optimal algorithm of determination of the inclination angle of an unprepared landing pad such as: the statistical characteristics of the inclination angle’s estimation of an unprepared landing pad and the estimation of a time complexity of the proposed optimal algorithm of determination of the inclination angle are presented. The verification of the developed optimal algorithm of determination of the inclination angle of an unprepared landing pad with the SRTM opensource digital elevation map and the OpenStreetMap web mapping service is completed. 
Ivanenko K. A., Egorov S. I., Borzov D. B. Algorithm for calibration and adjustment of air signal system elements. Trudy MAI, 2023, no 132 The aircraft position determining in the airspace is is one of the key and important components of navigation. An important subtask herewith for achieving the goal is altitudes, speeds and accelerations determining, since the specified trajectory cannot be maintained in the absence of these parameters. The main types of the employed radio altimeters are the barometric and radio altimeters. Instruments based on the principle of computing the return time of the signal reflected from the Earth are employed for the most part while the aircraft takeoff and landing, while for the most portion of the flight, the work is being performed by the barometric instruments. The pressure sensors readings are being affected by the ambient temperature. They are divided into compensated and uncompensated by the principle of dependence on temperature. Temperature compensation of the sensor implies the return of the sensor to the readings that it would give without accounting for the temperature effect, after a certain time and with a certain error. The basic compensation properties, such as error and return time, can also depend on temperature factors in practice and vary over the temperature range. Besides, sensor membranes are subjected to aging, and the temperature compensation properties of sensors may depend on the wear factors as well. In case of employing sensors without compensation, all the work on temperature correction of readings is performed by a mathematical apparatus, which is based on the readings of the sensors themselves, as well as on the readings of a number of other sensors that measure the properties of the environment. When applying sensors with temperature compensation, the mathematical apparatus can perform thermal correction operations at the boundary sections of the temperature range. Besides the temperature correction, mathematical apparatus in air signal systems is required to compensate for the static pressure error, which increases with the measured altitude increasing. Thus, with deviations of 0–5 meters in the altitude range of 0–1000, in the range of 4500–5500 meters, the error may already be of 15–25 m, which is unacceptable in the requirements for modern airborne signal systems (Air Signal System). The main problem of dynamic pressure sensors is opposite to the static data, namely it consists in in error values increasing at low speeds of 0–75 m. Besides, this device should be insensitive to the wind interference in a stationary state on the ground, so as not to interfere with the other equipment operation. With the speeds growth, the in error increase is not as obvious as at low speeds. The above said problems demonstrate the relevance of creating an algorithmic and mathematical apparatus for preliminary calibration of the SHS systems, a calibration methodology, as well as a system for its hardware support. The object of study of this work is methods for calibrating the temperaturecompensated static and dynamic pressure sensors, forming the air signal system. The subject of the study is a mathematical apparatus for bringing the readings of barometric sensors into specified ranges. As a result of the design, the following was accomplished: – an algorithm for calibrating static and dynamic pressure sensors has been developed; – a method has been formulated for reducing the natural curve of sensor readings to the reference ones; As the result, a mathematical model, algorithm and calibration technique are proposed with subsequent mathematical correction of the readings of temperaturecompensated sensors of the SHS system, based on an analysis of the behavior of selected sensors when changing functional and temperature ranges, using modern technological equipment. A method for calibrating air signal sensors has been developed and debugged, allowing performing input control of the employed sensors, identifying in advance devices with an inoperative compensation apparatus, by analyzing data obtained by simulating flight conditions. The authors developed iterative algorithms for interaction between the traffic controller and the hardware and software complex that implement the existing methodology. 
Fetisov E. V., Zimnikov D. V. Model of performing periodic maintenance at the complex with unmanned aerial vehicles. Trudy MAI, 2023, no 132 This article presents an approach to developing a model for performing periodic maintenance on unmanned aerial vehicle complexes. The active use of the complexes is accompanied by research aimed at improving the methods of use, increasing the tactical and technical characteristics, but not given issues of performing various type of maintenance, their modeling and evaluation, despite the existing contradictions in theory and practice. When organizing of periodic types of maintenance it is necessary to take into account a large number factors that can affect the timing and quality of work. Simulation modeling is one of the most effective tools for studying complex systems today. Imitation is a kind of means of reproducing phenomena, just as a model is an abstract description of a system, object, phenomenon or process. That is, modeling is such an abstract form of reflection of reality, in which certain properties of the proposed objects are represented in the form of an image, a diagram, a plan, or a complex of equations, algorithms and programs. The use of simulation modeling in many fields of activity has a number of undeniable advantages. Firstly, it is an experimental method of cognition, which is a simple and visual tool for analysis. It helps to find optimal solutions to problems and gives a clear idea of complex systems. The simulation model of the process of organization and performance of periodic maintenance of a complex with unmanned aerial vehicles is developed in Arena system, allowing to make rational decision on the selection of maintenance performers, to assess the workload of specialists, as well as to form requirements for a rational composition of the necessary maintenance tools. 
Averyanov I. O. Mathematical model of nondeformed cargo parachute landing system with dampers on rigid plane in case of stationary wind field. Trudy MAI, 2023, no 131 This article describes the mathematical model (MM) that extends MM of cargo parachute vertical landing system with dampers process on rigid plane developed in [1] to the case of its landing with horizontal velocity. The aim of the research is to update the model of statistical modelling of cargo landing process [2] to the case of its parachute landing. Wind effect is the main reason of parachutecargo system (PCS) horizontal velocity. In this article the stationary wind field is considered. The overturning moment is applied to the cargo in case of its parachute landing with horizontal velocity. One part of the moment comes to the cargo from its lower part due to frictional effects when it contacts to the plane. This effect considered in [1] and [3] and is taken into account in this MM. The second one – comes from the parachute system and passes through the suspension system to the cargo structure. Therefore, to get the overturning moment correctly the following changes are added to the MM [1]: multiple canopy parachute system (MCPS) instead of the equivalent canopy, suspension system and the parachute unlocking system (PUS). MCPS is commonly used for heavy cargos parachute landing, that’s why the MM of MCPS is developed. It consists of separate inertial canopies with elastic slings. The canopies can receive the aerodynamics loads and have elastic contacts to each other. The MM of suspension system consists of elastic links joined through the point inertial elements. PUS is modelled with the special condition to the correspondence suspension system link. The wind field is modelled by aerodynamics loads applied to the canopies of MCPS and the cargo. The task of parachute horizontal landing of cargo with dampers is considered to demonstrate the influence of parachute system to the landing process. Analysis of the results makes it possible to conclude that the developed model shows the plausible characteristics of the landing process and can be used in [2]. 
Gerasimchuk V. V., Zhiryakov A. V., Kuznetsov D. A., Telepnev P. P. Simulation of the vibration background of the spacecraft. Trudy MAI, 2023, no 131 As pulses exchanging units, flywheel engines and correcting engines play the part of a fundamental component of the majority of spacecraft for both coarse orientation control and precise guidance. The rotating masses’ unbalance while flywheels engines operation and force vibration impacts caused by pressure pulsations in the combustion chamber of correction engines are able to cause excessive fluctuations of the research equipment, which may lead to a in the functioning accuracy decrease. The vibration load levels are being determined during the spacecraft experimental testing. However, it seems rational to select optimal places for the highprecision equipment installing by their vibration background modeling at the early design stages to minimize the level of their vibration load. The vibration background was being determined for the developed finite element model of the spacecraft «flexible» design with the environment of the Femap with NX Nastran software package. Computations were performed for vibration loading options by one of the four enginesflywheels, and from the two correction engines. The model of the by the flywheel engine exposure accounted for the forces resulting from the flywheel imbalance. A harmonic action with an amplitude proportional to the square of the flywheel rotation speed was being modeled. The vibration load levels from the correction engines disturbing forces were studied for both inphase and outphase cases of the exposure. The study was being performed by the harmonic analysis method. The values of the disturbances amounts corresponded to the levels of disturbances of the standard flywheel engines and correction engines. The vibration load levels assessment in the places of the supposed fixing of the devices was being performed according to the maximum values of the computed linear and angular vibration accelerations, angular velocities and angular displacements along the three axes. The vibration background modeling option of the of installation sites of the equipment sensitive to the position stability for its effective operation presented in the article allows for a preliminary assessment of the vibration load level of such equipment at the early stages of a spacecraft design. 
Popov I. P. Dynamic properties of a dispersed material under harmonic vibrations. Trudy MAI, 2023, no 131 The aim of the work is to establish the dynamic properties of a dispersed material with harmonic vibrations. In strength calculations of structural elements of aircraft, among other things, modes of forced and natural vibrations are taken into account. In this regard, the dynamic properties of the transported cargo are taken into account, which are significantly different for solid and dispersed materials. The research methodology consists in presenting the status of the system under study as a combination of its diametrically opposite limiting statuses. Considered is a dispersed material located on a platform that performs harmonic oscillations. To assess the instability (or stability) of a dispersed material relative to the platform, a dimensionless quantity ξ is introduced. Its limiting values are ξ_{a} — absolute stability (complete immobility) relative to the platform and ξ_{z} — absolute instability. The main problem in establishing the dynamic properties of a dispersed material is the impossibility of calculating the average coefficient of dynamic friction, since its value is influenced by the interaction of dispersed particles with each other in the entire mass of the material, and not only with the surface of the platform. The description of the dynamic status of a dispersed material in the form of a composition of its unstable and stable statuses provides the key to solving this (and similar) problems. Opposite limit statuses of the system under study can be comparable and incomparable in terms of quantitative assessment. The subject of the study are systems with equal limiting statuses. The proposed method is universal and applicable to a wide variety of systems with different statuses and parameters. 
Ledkov A. S. Dynamics and control of cylindrical space debris during contactless ion beam assisted transportation. Trudy MAI, 2023, no 131 Space debris poses a serious threat to existing and newly launched spacecraft. One of the prospective ways to this problem solving consists in creation of contactless transportation systems based on the ion beam application generated by the electric thruster of an active spacecraft to affect a space debris object. The purpose of the work is efficiency increasing of the space debris ion beam assisted transportation by accounting for its motion relative to the center of mass specifics. The author developed mathematical models describing a space debris object motion under the impact of gravitational and ion forces, as well as torques for the plane and spatial cases. The study of the unperturbed motion of a space debris object in a circular orbit was performed. The author proposed the ion bean control laws ensuring the space debris stabilization in the equilibrium position and its transition to the required angular motion mode. Angular modes of the unperturbed motion, at which generated ion force was maximum and minimum were determined. Numerical modeling of the space debris object disorbiting was performed, and estimation of the fuel consuming necessary for this transportation operation accomplishing was given. For the space debris object being considered, the difference in fuel between the most favorable and unfavorable angular motion modes was 7.82%. 
Zuskova V. N., Okonechnikov A. S., Serdyuk D. O. Transient dynamics of a thin isotropic spherical belt. Trudy MAI, 2023, no 131 Thinwalled spherical shells are common structural elements in various industries, such as aircraft, rocket and mechanical engineering. When designing the corresponding structural elements, one of the topical issues is the calculations of structures operating in nonstationary interaction modes. Such calculations are complex and timeconsuming, since in such problems the desired solution is significantly heterogeneous in spatial coordinates and time. In an axisymmetric formulation, the study of the transient dynamics of a thin spherical belt with emission boundary conditions under the influence of a moving transient load. The belt material is elastic and isotropic. The KirchhoffLove hypothesis was implemented in the qualitative mathematical model of the spherical scenario. An approach to research based on the principle of superposition, the Green’s function method and the method of compensating influence. The essence of the results is in connection with the desired solution with the acting and compensating load using integral operations such as convolution in coordinate and time. Being this operation, is the Green’s function for spherical exploitation, which is the normal displacement in response to the core, random focusing on the load coordinate and time, mathematically described by the Dirac delta function. The compensation solution is the result of studying some specially calculated values, at which decisions are made from the acting load and the compensating sensation, satisfying the boundary conditions at the ends of the spherical belt. An example of calculating the unsteady dynamics of a spherical belt is given. The results for transient functions of normal displacements, angles of turns and bending moments are presented in the form of graphs. The method of compensating loads applied in the work allows us to study the transient dynamics of a spherical belt with intermediate axisymmetric supports, as well as spherical segments. 
Korovaytseva E. A. Postcritical behavior of hyperelastic cylindrical shell. Trudy MAI, 2023, no 131 The work studies the process of local inflation of cylindrical shell made of hyperelastic materials of different types under the action of uniformly distributed pressure and axial force. Mathematical statement of the problem includes 4 quasilinear differential equations and 9 nonlinear algebraic equations. Geometrical relations of thin shells nonlinear theory are used, and for nonlinear physical relations formulation elastic potentials of different types are involved. The problem is solved using parameter differentiation method algorithm. According to this algorithm, resolving nonlinear equation system is differentiated with respect to solution continuation parameter, which leads to forming interconnected quasilinear boundary and nonlinear initial problems. These problems are solved in steps using iteration method until reaching required proximity of prognosed and corrected solutions at each parameter step. At given loading type and boundary conditions for the shell of constant thickness components of its stressstrain state will be constant along the meridian at any value of internal pressure. However it is known that at uniform inflation of cylindrical shell after reaching load critical value bulging can occur under certain conditions. For obtaining corresponding numerical result an assumption of small local thinning of shell wall was introduced. Two types of shell material were considered — neohookean and Yeoh. The diagram «pressure — relative volume change» for the case of neohookean cylinder inflation has only one maximum. Postcritical deforming of a shell with local thinning in this case differs fundamentally from the one of a shell with constant thickness. Differences are observed both in loading diagrams and character of stressstrain state components distribution along the whole meridian. Meridian of the shell with local thinning buckles at the largest part of its length. The diagram «pressure — relative volume change» for the problem of inflation of a cylinder made of Yeoh material has a local maximum and a local minimum. Distribution of stressstrain state components along the meridian remains constant both for the shell of constant and variable thickness, in the last case changing insignificantly only along the segment with local thinning. Meridian of the shell with local thinning remains straight. Thus introduction of an assumption of hyperelastic cylindrical shell local thinning for the case of loading by uniform pressure and axial force allows investigating theoretically the character of its postcritical behavior corresponding to experimentally observed one. 
Sazanov V. P., Kirpichev V. A., Pismarov A. V. Distribution of residual stresses in bottom of thread after advance surface plastic deformation. Trudy MAI, 2023, no 131 The article presents the results of computingandexperimental study of the advance surface plastic deforming impact on stress fatigue strength of the parts with M16´2 metric thread, produced from the 30HGSA and 40X structural steels. The surface of cylindrical workpieces was hardened by rolling on the roller worktool prior to the thread cutting. Computations of the residual stresses distribution in the lest sections of the thread vees were performed by both analytical and finite element modeling methods. It was found that that these results demonstrate rather high convergence in the thread vees slightly removed from the start of the threaded portion of the part. Obviously this is associated with the fact that an analytical solution of the residual stresses distribution was performed at a quite long distance from the rim zone. Finite element modeling and necessary computational volume were performed employing the PARTRAN/NASTRAN software complex. Finite element models of the smooth cylindrical and threaded pieces were developed in the axisymmetrical setting, and residual stressstrain state modeling was conducted by the thermoelastisity method using initial deformations. The squeezing residual stresses impact on the fatigue resistance was being determined through the endurance limit increment by the mean integral stresses criterion. Calculating increments of the endurance limits were compared with their experimental values obtained while fatigue tests of hardened and nonhardened threaded pieces at the rotational bending in the case of the symmetrical cycle (30HGSA) and stretching in the case of asymmetrical cycle (40X). Accounting for the close increments values of the endurance limits at bending and limiting amplitude of the cycle while bending the important inference on the stretching substitution by bending while fatige test conducting is confirmed. 
Dmitriev V. G., Popova A. R. Mathematical modeling of panels and arches stressstrain state for the case of large displacements and strains at designing thinwalled aircraft structures of hyperelastic materials. Trudy MAI, 2023, no 131 The presented work is aimed at mathematical models and computational algorithms developing for studying specifics of deformation processes of the panel and arc structures from hyperelastic materials at arbitrary displacements and deformations. The initial continual problem discretization by the spatial variables is being accomplished by the finite difference method with approximation of differential operators by the finite differences of the secondorder accuracy. Quasidynamic form of the settling method with plotting an explicit twolayer difference scheme by the time of second order accuracy is being employed for building the nonlinear boundary problem solving computational algorithm. The stressstrain state specifics were studied and critical loads values were determined for the locally loaded arc structure from the hyperelastic material while using the relationships of the MooneyRivlin model neo Hookean model for both fastened and hingefixed edges. 
Nikitchenko Y. A., Berezko M. E., Krasavin E. E. Comparison of the NavierStokesFourier model and the twotemperature model on the example of the problem of flow around high camber surface. Trudy MAI, 2023, no 131 The problem of flow around a surface with a large curvature (sharp edge) is becoming very relevant in connection with the development of modern technologies. In the vicinity of a sharp edge, a highly nonequilibrium gas flow occurs. Depending on the sharpness (curvature of the surface) of the edge, the degree of nonequilibrium of the flow can approach the nonequilibrium in the shock wave. In the present work, we consider a supersonic flow of a diatomic gas around a plate of infinite span, which is installed parallel to the oncoming flow. The tip of the plate is rounded. The rounding radius characterizes the Knudsen number Кn of the problem being solved. The aim of this work is to estimate the maximum value of Kn at which the solutions of the NSF and M2T models practically coincide. The calculations were carried out for a diatomic gas at the Mach number M=2. The Knudsen number varied in the range Kn=10^{–2} ... 1. In the framework of the problem under consideration, Kn can be considered as the degree of pointedness of the nose, regardless of the degree of rarefaction of the gas, which is traditionally characterized by the number Kn. The most important gas parameters, from a practical point of view, are the density and temperature in the nearwall region. These parameters mainly determine the processes of erosion of the edge surface, leading to a change in its shape. The performed calculations show that for Kn>10^{–2} both models of the first approximation, which describe the energy exchange between the translational and rotational degrees of freedom in different ways, lead to significantly different temperature distributions. the temperature distributions are fairly close over the entire range of Knudsen numbers considered. 
Khatuntseva O. N. Accounting for entropy production in the system of NavierStokes equations when describing the turbulent flow of a viscous compressible heatconducting liquid. Trudy MAI, 2023, no 131 To describe both laminar and turbulent flow regimes of a viscous incompressible non—heatconducting fluid based on the same equations, the references [13] proposed to account for what distinguishes these two regimes from each other, namely the entropy production due to the random stochastic perturbations excitation. For this purpose, the NavierStokes equations (NSE) were written in a phase space expanded by introduction of an additional stochastic variable. As the result, in the left part of the equations, namely in expressions for the total time derivative, additional terms, characterized by the entropy production due to the excitation of stochastic perturbations, appeared. For laminar flow modes, entropy production adopts a zero value, additional terms vanish, and transition to the NSE in their standard form, of which solutions describe only laminar flow modes, is accomplished. Inclusion of an extra summand in the expression for the total time derivative, characterized by entropy production (which is always nonnegative), allows, in particular, accounting for the irreversibility of physical processes in time in cases where this production is nonzero. The above said applies, among other things, to the case when large values of the Reynolds number are realized and, accordingly, the value of the viscous term in the NSE tends to zero. In this case, the only term of the equation «responsible» for its irreversibility becomes an additional term in the full time derivative. Solutions corresponding to laminar and turbulent flow regimes have been obtained analytically for HagenPoiseuille problems, planar Poiseuille flow and planar Couette flow. Experimental. Comparison of experimental and analytical solutions for different values of the Reynolds number was performed. The presented article considers a more general case, using a similar approach, namely analyses how the equation of continuity; NavierStokes equations; the equations of total conservation of energy, and heat transfer should change, when describing the flow of a viscous compressible heatconducting fluid, in which stochastic disturbances may occur in a wide range of scales at large values of the Reynolds number. 
Vavilov V. E., Ismagilov F. R., Mustaev E. I., Urazbakhtin R. R. Numerical study of the enginepropeller combination of the unmanned aerial vehicle with the propeller integrated into the engine. Trudy MAI, 2023, no 131 The article presents a proposal for application of the improved enginepropeller group with the airscrew integrated into the electric motor in the multirotor type unmanned aerial vehicles. The authors performed a checkup aimed at confirming the proposed technical solution operability, which was realized by the presented modification comparison with classical scheme of the enginepropeller group. The juxtaposition was being accomplished by the aerodynamic characteristics of the airscrew in the hovering mode by the computational hydrogasdynamics methods with the STAR CCM+ and ANSYS CFX application software. Numerical modeling was performed in the 3D setting and based on solving the system of Reynoldsaveraged NavierStokes equations, which were closed using the turbulence models of the KEpsilon family. The airscrew rotation was described by the moving frame of reference without the grid changing. The data obtained from the mathematical study indicate a noncritical reduction in the lifting force of the improved scheme of the enginepropeller combination group compared to the traditional one, and are fixed at 3.9% and 2.5% in ANSYS CFX and STAR CCM+, respectively. The drag torque of the airscrewof the modified scheme increased by 0.741% relative to the classical one when modeled in the STAR CCM+, and decreased by 0.944% when modeled in the ANSYS CFX. The proposed scheme weight herewith, computed in SolidWorks, decreased by 8%. The results of the performed checkup are satisfactory and prove the applicability of the improved scheme of the enginepropeller combination in unmanned aerial systems to increase their reliability, as well as reduce weight and dimensions without the risk of malfunctions in their operation. 
Babich E. V., Kolesnik E. V. The influence of geometry on a supersonic laminar flow past a bluntfin body mounted on a plate. Trudy MAI, 2023, no 131 The study of the flow structure near an obstacle mounted on a streamlined surface and the correct prediction of heat transfer characteristics is important both for practical purposes, in particular, in the aerospace industry, and in fundamental and theoretical respects. Such flow results in a highly threedimensional flow pattern, which includes an elongated flow separation region containing a set of horseshoeshaped vortices and a complex shockwave interaction. This paper presents the results of a numerical solution of the problem of supersonic flow past a blunt fin mounted on a plate with a developing boundary layer. In most works on this topic, the flow around bodies of simple geometry is studied, however, objects with a more complex configuration are of interest for practical purposes. This work, which is a continuation of research [12], is devoted to studying the influence of the geometric shape of the obstacle (slope angle, shape of the leading edge) on the flow structure and local heat transfer characteristics; herewith cases of flow leakage at different angles of attack are considered. In our calculations, we used the SINF/FlagS finitevolume unstructured code developed at Peter the Great St. Petersburg Polytechnic University. We solved the complete 3D Navier—Stokes equations for a thermally and calorically perfect gas. According to the research, in supersonic flow around a body mounted on a plate, such changes in the geometric configuration as narrowing of the leading edge, a decrease in the slope angle, and asymmetric flow lead to a reduction in thermal loads caused by the effects of viscousinviscid interaction. 
Tarasov A. L. Flow characteristics in the operational range angles of attack and Mach numbers numerical investigation of helicopter airfoils. Trudy MAI, 2023, no 131 The article presents the results of calculation of distributed and integral aerodynamic characteristics of helicopter airfoils NACA0012, NACA23012, VR12 and HH02 in the operational range of changes in angles of attack and Mach numbers, obtained by numerical simulation based on RANS. Modeling of helicopter airfoils flow was carried out considering the presence of a laminarturbulent transition in the boundary layer on their surface, the presence of disruptive phenomena and compressibility of the flow. Calculations were performed by using the ANSYS Fluent software package. The results obtained are satisfied with the data of known experimental studies. The description of the features of finitedifference mesh used for calculations, boundary and initial conditions, turbulence models, solver settings is given. The distributed aerodynamic characteristics of the airfoils are presented in the form of coordinate diagrams of the distribution of the pressure coefficient over their contours. Integral airfoils aerodynamic characteristics are presented in the form of graphical dependencies and diagrams. According to the results of the calculations, the patterns of behavior of the distributed and integral aerodynamic characteristics of the studied airfoils are revealed when the flow conditions change in the entire possible operational range of operation. The comparison and comparative analysis of the studied airfoils characteristics determining their aerodynamic perfection are also given. The results of the work can be used in the development of helicopter profiles, direct and inverse problem solution to optimize their shapes, as well as in the process of performing calculations to determine the aerodynamic characteristics of helicopter propeller blade airfoils by CFD methods in the entire possible operational range of their operation at angles of attack and Mach numbers. 
Piganov M. N., Kulikov A. V., Novomeisky D. N. Predictional mathematical models of thinfilm elements of microassembly. Trudy MAI, 2023, no 131 The lion share of the onboard equipment failures (up to 70%) is stipulated by the inadequate reliability of the onboard equipment electronic parts base. One of the effective ways to improve the onboard radioelectronic systems quality consists in selecting highly reliable elements and components based on the results of diagnostic control or individual prediction (IP) of their future state. This is especially true for the devices and elements, such as thinfilm microassemblies with highprecision resistors and capacitors. One of the most important operations in such microassemblies manufacturing is the thinfilm elements trimming to the nominal value. However, this trimming operation often introduces a perturbing effect into their structure, which reduces the temporal stability and reliability of these elements. This makes the procedure for rejecting potentially unreliable elements and selecting highquality samples for the onboard equipment (the IP based) especially uptodate. Mathematical models are proposed for individual prediction of quality and reliability indicators of microassembly thinfilm resistors and capacitors. An expert survey was conducted to select the forecasting method. With account fort the fact that informative parameters were previously identified for the class of microassemblies and thinfilm elements under study, the following methods of pattern recognition theory were selected as the main ones: the method of discriminant functions, potential and regression functions (models), as well as the extrapolation method. The latter was emplooyed for the case of low information content of the parameters. Forecasting effectiveness estimate based on the proposed models is presented. The developed models are recommended to be applied for solving problems of individual prediction of elements with classification. 
Nenashev V. A., Afanasyeva V. I., Zalishchuk A. A., Grigorov M. Y., Morozov A. V. Formation of threedimensional terrain models based on lidar survey to identify structural changes in the earth's surface. Trudy MAI, 2023, no 131 As of today, development of highprecision digital terrain model based on data of the smallsized onboard laser system for environmental state control is an uptodate task. Detection of temporal changes in the landscapes of the controlled zones in dynamics may relate to such tasks. In this case, plotting the highaccuracy 3Dmodels of the terrain may be accomplished by the data of the smallsized onboard laser system, collected in the current time instant with the archive data free from the current changes. The multitemporal digital models plotting of the terrain allows rather distinctly outline season changes, such as fire zones detection, the size of the coast brim size of rivers, lakes and other impoundments, as well as the scales of the swamp terrain forming, ice melting, snow covers and other temporal changes. Such approach employing for highlyprecise digital terrain model separated by time based on complex procession of the initial laser data collected from small UAVs is applicable for the purpose of environmental control, particularly for revealing structural changes of the various themes registered objects, which is an important and uptodata task, particularly for various structures accomplishing searchandrescue operations, including the ice situation determining, as well as under Arctic conditions. The purpose of the presented work consists in conducting the experiment on the UAV application with the smallsized onboard laser system installed on it for obtaining lidar terrain data, which afterwards would be converted into 3D terrain models and employed for the environmental situation control of the definite sector of the Earth surface. The article considers an example of application of the 3D terrain model, created with the lidar data, to compare two terrain models created according to the same route assignment with the oneweek interval. The data on the structural difference of the Earth surface models taken off at the different time instants, which can be applied for studying the environmental situation of the registered section of the Earth surface were obtained. The results of the study may be employed while modernization of the conventional systems and development of the prospective systems for the environmental situation control of the certain section iiof the Earth surface. 
Ispulov A. A., Kalmykov A. V. Method for determining the initial conditions for the use of uncontrolled reactive ballistic bodies from mobile carrier. Trudy MAI, 2023, no 131 The problem of ballistics is the process of calculating the trajectory of an uncontrolled reactive ballistic body after it has been separated from the carrier. At present, the basis for calculating the trajectory is the canonical model of motion, which describes the change in velocity, nutation angle, angular velocity of nutation, trajectory inclination angle, and rocket coordinates. However, this model is adequate only in conditions of uniform rectilinear flight; when the carrier is maneuvering, additional corrections are made depending on the angles of attack and slip of the carrier. The accuracy of the use of unguided reactive ballistic bodies depends on the initial launch conditions, which are determined by the parameters of the carrier and target motion. Development of a methodology for determining the initial conditions for launching an unguided reactive ballistic body with a vertical maneuver of a movable carrier. A technique has been developed for determining the initial conditions for launching an uncontrolled reactive ballistic body with a vertical maneuver of a movable carrier, for which analytical expressions have been obtained to determine the initial values of velocity, nutation angle, angular velocity of the nutation angle, and trajectory inclination angle. The results obtained make it possible to obtain the dependences of the resulting initial velocity, the initial nutation angle, the initial nutation angular velocity, and the initial trajectory inclination angle on various conditions for launching an uncontrolled reactive ballistic body during a vertical maneuver of a movable carrier. The obtained experimental dependences can be used in the development of a ballistic algorithm to obtain the exact initial conditions necessary for integrating the differential equations of a complete ballistic motion model, which in turn will improve the aiming accuracy. 
Tarasov A. G., Milyaev I. K., Musienko A. S. A model for assessing the availability factor of electrical cable systems of space vehicles, taking into account the specifics of determining the technical condition. Trudy MAI, 2023, no 131 The article describes the methods, which are based on the concepts and relationships of probability theory and graph theory, to assess the impact of the switching number in the process of a cable network diagnosing on the availability factor employing the frozen coefficients method. The subject relevancy is being confirmed by the fact that more than 60% of electrical equipment has exhausted its operational life, and, with a view to the dynamics of aging, a more thorough diagnosis of its condition is required. The proposed methodology is based on the theory of probability and graph theory, as well as the basic concepts and relationships of the theory of reliability and technical diagnostics of systems. The initial data is information on technical condition of the power grid equipment elements of space vehicles in the course of the test control, information on the reliability (structural and logical diagrams, failure rates of elements) of technological power grid equipment, as well as diagnostic models that link the types of technical conditions and diagnostic signs of electrical equipment. When organizing of the electrical cable system control and restoring its performance, it is necessary to account for the number of switching electrical circuits, affecting significantly the electrical cable system readiness to perform tasks according to its direct purpose. In this regard, the obtained model for the availability factor assessing of the spacecraft electrical cable system allowed determining reduction in the duration of determining the technical condition of the electric cable system by 75%, and the availability factor increase of the spacecraft electric cable system by 1.7% through the adaptive switching application. The proposed model may be employed by specialists when performing control and diagnostic works of a cable electrical system with a view to increase their efficiency. The obtained model for the availability factor assessment of a spacecraft electrical cable system allows obtaining an adequate assessment of the availability factor with account for specifics of the technical condition determining, as well as comparing the efficiency various switching methods application for the electrical cable system diagnosing. Thus, an important point for ensuring the operable state of electrical equipment is adoption of a reasonable decision on its operational technical condition in connection with the individual characteristics of each piece of electrical equipment. The obtained data allow drawing up more reasonable plans for priority measures for the repair and renewal of electrical equipment based on the assessments of specialists working on the ground — experts, while improving the quality of management decisions. 
Dyachenko S. A. Automated verification complex for cockpit display systems of nextgeneration civil aircraft. Trudy MAI, 2023, no 131 According to accident statistics provided by international aviation authorities and leading airplane manufacturers, loss of control inflight stands as the primary cause of air crashes in terms of the number of victims. One of the contributing factors to loss of control inflight is the failure or malfunction of aircraft systems, which may result from undetected errors during the design phase. To address this issue, reducing the influence of the human factor in the development of onboard systems is crucial, and this can be achieved through the implementation of automation instruments. The article encompasses an analysis of verification automation tools for civil aircraft onboard systems currently available on the market, including formal verification and system testing instruments, as well as complex solutions. Moreover, the research highlights that the growth potential of these tools lies in graphic and aural information testing. This aspect becomes relevant when assessing the humanmachine interface within cockpit displays and flight warning systems verification. Additionally, the article proposes the architecture, algorithms, and software of such a complex providing text information recognition for cockpit display systems. The conducted tool testing confirmed its high effectiveness. While the complete exclusion of an operator from the verification process is deemed unacceptable due to safety concerns, the aforementioned type of tools can potentially enhance the humanmachine interface systems’ reliability by mitigating the influence of the human factor, and it can also lead to savings in time and financial resources. Concurrently, the underlying methods of computer image processing are universal, enabling the developed complex to be adapted to diverse technical systems featuring humanmachine interfaces (including industries beyond aviation). 
Minakov E. P., Privalov A. E., Bugaichenko P. Y. A method for estimating the characteristics of digital models of cyberphysical systems based on multiple regression analysis of the results of their application. Trudy MAI, 2023, no 131 Digital technologies implementation in the sphere of complex technical systems control has led to the advent of the cyberphysical systems (CPS) concepts and digital twins (DT). The DT basic element is the digital model (DM) of the CPS. Requirements to the DM characteristics are being confirmed while tests, verification and validation, to which ensuring the problems of substantiating the list of the DM characteristics and developing methods for their assessment are being solved. The article substantiates the choice of completeness and veracity of the DM as its target characteristics. A method for their assessment by the characteristics of the accuracy of the of the CPS properties estimates obtained with the DM, and the weighting coefficients determined employing multiple regression analysis of the DM application results is proposed. The said method is based on the analysis of the CPS target function, due to which the criterion applied in assessing veracity receives an obvious physical meaning. The proposed method may be employed for solving the problems of the DT structural and parametric synthesis, as well as analyzing their functioning effectiveness at all stages of the CPS life cycle. The result of the training stage is analytical models of the CPS characteristics, which can be used in optimization algorithms without significant requirements for computing resources. The training sample can be replenished while the DT exploitation which increases the accuracy of the DM characteristics assessment at various stages of the CPS life cycle. The adequacy of the method is confirmed by the presented in the article example of the DM characteristics evaluating of an angular motion control system with flywheel engines. 
Sentsov A. A., Korotkov V. A., Ivanov S. A., Turnetskaya E. L. Mathematical modeling of a free form inertial naigation system for airborne radar stations. Trudy MAI, 2023, no 131 Digital technologies implementation in the sphere of complex technical systems control has led to the advent of the cyberphysical systems (CPS) concepts and digital twins (DT). The DT basic element is the digital model (DM) of the CPS. Requirements to the DM characteristics are being confirmed while tests, verification and validation, to which ensuring the problems of substantiating the list of the DM characteristics and developing methods for their assessment are being solved. The article substantiates the choice of completeness and veracity of the DM as its target characteristics. A method for their assessment by the characteristics of the accuracy of the of the CPS properties estimates obtained with the DM, and the weighting coefficients determined employing multiple regression analysis of the DM application results is proposed. The said method is based on the analysis of the CPS target function, due to which the criterion applied in assessing veracity receives an obvious physical meaning. The proposed method may be employed for solving the problems of the DT structural and parametric synthesis, as well as analyzing their functioning effectiveness at all stages of the CPS life cycle. The result of the training stage is analytical models of the CPS characteristics, which can be used in optimization algorithms without significant requirements for computing resources. The training sample can be replenished while the DT exploitation which increases the accuracy of the DM characteristics assessment at various stages of the CPS life cycle. The adequacy of the method is confirmed by the presented in the article example of the DM characteristics evaluating of an angular motion control system with flywheel engines. 
Fetisov E. V., Zavyalik I. I. Assessment of the impact of operating conditions on technical condition of fuel system units aircraft engine systems. Trudy MAI, 2023, no 131 Requirements to aviation equipment operational properties are being tightened in the process of the aircraft functional systems improving, aimed at increasing flight reliability and safety levels. Despite substantial impact of the fuel impurity on the reliability of the fuel system units, this issue is still remains understudied. Despite the significant impact of aviation fuel pollution on the reliability of aircraft fuel system units, this issue remains insufficiently studied. This is especially true for establishing quantitative dependences of the probability of failurefree operation of the fuel system units most sensitive to the quality and purity of aviation fuel on the degree and nature of contamination and changes in the aircraft operating conditions. Conventional techniques for the aircraft fuel system failurefree assessment are based on the reliability factor values determining from statistical data on the results of tests and operation. It allows accounting for only the fact of the failure manifestation itself, but does not allow assessing such external factors impact as environmental conditions of aviation equipment operation and application, the impurity changing of the applied fuel effect on the probability of parametric failures and maloperation manifestation of the aircraft fuel system units. To solve this problem, the article presents a mathematical simulation model of the aircraft engine fuel system units functioning under various aircraft operating conditions developed with the MATLAB Simulink. The model allows studying and predicting technical condition of the aircraft engine fuel system units depending on changes in the aircraft operating conditions. For this, the dependence of the key parameters values of the fuel system on the impurity particles size and concentration in the aviation fuel in various conditions of the aircraft operation is being embedded into the system of equations, describing the aviation engine fuel system functioning based on the aggregative approach. The developed model application at conducting studies on the fuel units operability assessment with ranges expansion of input and internal parameters values (fuel system units of the aircraft power plant) will allow obtaining reliable assessment of the fuel system technical condition at the aircraft operating conditions changing. 
Pavlov D. A., Popov A. M., Tkachenko V. V. A model for correcting the initial marking of a classical Petri net based on solving a discrete programming problem. Trudy MAI, 2023, no 131 Apparatus based on the classical Petri net is being employed quite often while modeling various parallel asynchronous processes. This apparatus allows demonstrating the system transition from state to event, establishing causeandeffect relations between the states of the system being modeled. It offers an opportunity to perform formal analysis of the model properties and reflect the results of the obtained analysis on the real properties of the system. However, when the modeled system volume is large enough, and Petri net properties analysis produces incorrect result, changes should be introduced into the formed model, though detecting the place, which requires correction, is not an easy task. It will be necessary to analyze relations between all positions and transitions together with initial, intermediate and final marking stagebystage, namely from the initial to the final state. This article proposes a formal approach to the initial marking correction of the Petri net so as the network would reach the final state, i.e. correct fulfilling of the reachability property of the network by solving the discrete programming problem. The discrete programming problem will be solved in the case of the Petri net reachability property unfulfillment, i.e. when the reachability equation solution will differ from X ∈ Z^{n}. After the necessary solution finding, the reverse conversion operation of the system of linear equations into the reachability equation is being accomplished to discriminate the corrected vector of the initial marking from it. Correction of the initial marking vector is necessary for the net transition to the required (final) state. The said approach may be employed for various type initial data correction, as well as corrections of the quantitative components of separate states of the system being modeled. 
Kasatikov N. N., Brekhov O. M., Nikolaeva E. O. Integration of artificial intelligence and the Internet of things for advanced monitoring and optimization of energy facilities in smart cities. Trudy MAI, 2023, no 131 Energetics is one of the most important and stateoftheart topics of the contemporaneity. Energy facilities monitoring and optimization play decisive role in ensuring effective energy consumption and sustaining stable infrastructure in the fastdeveloping cities. Energy facilities optimization with the artificial intelligence (AI) and Internet of things (IoT) technologies plays an important role in ensuring effective energy consumption and sustaining stable infrastructure in the fastdeveloping cities. New innovative technologies allow data collecting in the realtime mode, performing enhanced analytics and accomplish intellectual decision making, which leads to the energy efficiency enhancing, operational costs reduction and stability increasing. One of the energy facilities monitoring advantages using AI and Iot consists in the possibility for energy consumption optimization based on the demand, weather conditions and other factors. The AI algorithms are able to analyze collected data and predict energy requirements, which allows reducing electricity bill and negative impact on the environment. The algorithms may simplify the air traffic controllers tasks while civil aircraft landing or departure. The IoT units, i.e. sensors and intellectual counters, are being installed at the energy facilities and civil aviation industry objects for real time data collection on various parameters, such as temperature, pressure, voltage and output power. These units transmit data to the central monitoring system, allowing operators surveying the energy facilities operation and indicating any deviations from the normal operation conditions. The AI algorithms, machine learning and deep learning models can analyze the data collected by the IoT units to detect anomalies and anomalous regularities. The researchers may study the normal operating behavior the energy facilities by training the AI models using the test data. When the collected data deviate significantly from the expected values, the AI system may issue warnings to notify operators about potential problems or malfunctions requiring their attention. AI and neural networks may be employed for predicting demands for servicing and preventing unexpected damage at the energy facilities and civil airports. By the data analysis from the IoT sensors and units, the AI models can reveal regularities pointing out potential failures or productivity reduction. It allows operators planning technical servicing in advance of repairing equipment prior to the failures and minimizing the downtime. The AI algorithms can as well optimize operation of the energy facilities and enterprises of civil aviation trend by the real time data analyzing and revealing the possibilities for the efficiency enhancing. The AI, for example, may analyze the energy consumption schemes, the data on the equipment productivity and external factors, such as weather conditions, for energy systems optimal control and energy consumption reduction. Thus, the Ai and IoT technologies application for energy facilities and civil aviation objects monitoring and optimizing demonstrate many advantages, including energy efficiency enhancing, power consumption costs reduction, stability improving and reducing negative impact on the environment. These innovative approaches help municipal companies, power suppliers and objects managers make justified decisions, develop strategies and ensure longterm stability of energy facilities in the rapiddeveloping cities. 
Kuznetsova S. V., Semenov A. S. Digital twins in the aerospace industry: an objectoriented approach. Trudy MAI, 2023, no 131 The increasing complexity, versatility and uniqueness of aerospace products require new efficient approaches to their design and operation. It is expected that the use of digital twin technology will effectively solve emerging problems. In the publications and data sources, the concept of a digital twin is given quite a lot of definitions. The national standard GOST R 57700.37–2021, adopted in 2021, defines the digital twin of a product as follows: «A system consisting of a digital model of a product and twoway information links with the product (if the product is available) and (or) its components.» In the aerospace industry, there are the following features of creating digital twins:
The creation of a digital twin largely depends on the methodology of development, production and operation. It becomes relevant to create a software and technological platform for the production and use of digital twins in the aerospace industry, taking into account life cycle processes (according to GOST R 56135). A platform for creating digital twins should support the proposed methodology, methods for integrating physical objects with the Internet of Things, and graphodynamic description of simulated objects. The article explores the technology of developing digital twins in the aerospace industry. The main features of creating a digital twins in the aerospace industry have been determined. Fundamental technologies for the implementation of digital twins have been considered: Iot, XR, Cloud computing, AI, quantum modeling, cybersecurity. A fractal approximation methodology has been proposed for the development, production and operation of digital twins based on elastic objects, as well as a platform architecture for creating digital twins. The article considers incremental objectoriented development, production and operation of digital twins in combination with a graphdynamic description of physical objects and methods of the Internet of things. Efficiency is achieved through the reuse of software and hardware components, surrogate models that integrate physical objects with the Internet of things and graphodynamic description of simulated objects. 
Popov I. P. Additive energy constant of gravitational interaction. Trudy MAI, 2023, no 130 The article presents definitions of the total stored energy, conditional stored energy, conditional realizable stored energy, and conditional unrealizable stored one. The total stored gravitational energy is the energy of a system or object equal to the maximum work that the system or object can perform if offered the opportunity to do so. A system or an object with zero total stored gravitational energy cannot perform any work. A system of two massive balls has zero total stored gravitational energy when their centers are aligned. The latter is possible if the balls are mutually penetrating, for example, discontinuous, particularly, accomplished in the form of layered joints. Conditional stored gravitational energy is a part of the total stored gravitational energy of a system or object, limited by the condition, which excludes the possibility of the system or object to perform maximum work that the system or object can hypothetically perform. Conditional realizable stored gravitational energy is a part of the total stored gravitational energy of a system or object, equal to the work that the system or object can perform, limited by the condition that excludes the possibility of the system or object performing the maximum work that the system or object can hypothetically perform. Conditional unrealizable stored gravitational energy is a part of the total stored gravitational energy of a system or object, equal to the work that the system or object cannot perform, limited by the condition that excludes the possibility of the system or object performing the maximum work that the system or object can hypothetically perform. 
Akentyev A. S., Fokina A. A., Makarov D. K. Mechanical analysis for optical retroreflector antenna system for highorbit segment of glonass navigation system. Trudy MAI, 2023, no 130 The article presents options of the retroreflective antennae system (RRAS)for the spacecraft of the highorbit space complex of the GLONASS system. The options of the structure with various arrangement of orifices, the number of angle reflectors and other constituent parts were analyzed. The structure of the optical retroreflectory antenna system meeting the requirements for successful leading out as a part of the spacecraft and functioning at the obit of the 36000 km altitude. Mechanical analysis of the selected structure was performed. Analysis of the eigen frequencies of the structure confirmed the absence of resonance between the constituent parts of the spacecraft and RRAS. The study of the stresseddeformed state of the structure revealed that the largest calculated stress in the structure was less than the permissible value, which ensures the RRAS strength margin enough for the system successful leading out as a part of the spacecraft on the working orbit. As long as there are no eigen frequencies less than 100 Hz in the structure, the level of the sinusoidal impact amplitude is equal to the amplitude of the quazistatic impact. The RRAS persistency to mechanical loads impact at the segment of leading out the spacecraft by the booster was confirmed. 
Grishakin V. T. Deformation of the elastic pendulum thread at resonance. Trudy MAI, 2023, no 130 The article deals with the problems of free plane and spatial oscillations of a spring pendulum at the frequencies ratio of linear and longitudinal oscillations leading to resonance. Various mathematical models of the studied mechanical systems are adduced, and numerical results obtained when using them are compared. The author proposed a simplified model of a flat spring pendulum, which application is possible in solving engineering problems. The article illustrates the effects of the swing energy «pumping» into the axial oscillations energy of the pendulum and rotation of the pendulum material point trajectory around the vertical axis at a resonance of 1 : 1 : 2. It is established that with different frequency ratios of linear and longitudinal oscillations, the specified effect of the oscillation energy «pumping» is not observed. The effect of the swing plane rotation herewith remains, but manifests itself to a lesser extent. The trajectories of the first 20 s of the material point of the spatial spring pendulum movement at resonances were compared 1 : 1 : 2, 1 : 1 : 3 and 1 : 1 : 5. Maximum values of the thread relative deformation depending on the initial conditions of the problem under consideration are adduced for the first computational case. Computational results are summarized in a table allowing evaluating the largest relative deformations of the pendulum thread depending on the initial deviations from the equilibrium position and initial impulses, which resulted in the processes under study occurrence. 
Pronina P. F. Analytical modeling of heat transfer in the elements of the screenvacuum thermal insulation. Trudy MAI, 2023, no 130 The article deals with analytical modeling of the screenvacuum thermal insulation elements (SVTIE) for temperature distribution determining in the composite thermal protection coating. Screenvacuum thermal insulation is widely used in aerospace engineering, namely in the automatic interplanetary stations, spacecraft, satellites, fuel tanks of launch vehicles. The study of this type of thermal insulation is of prime importance for ensuring safety and service life of aerospace complexes elements throughout their lifetime. High reliability requirements are stipulated by the thermal protection operation under conditions of temperature fluctuations and prolonged exposure to solar radiation. The article considers a fourlayer structure in the onedimensional formulation with the solution of the unsteady thermal conductivity problem based on a twolayer homogeneous rod. The fourlayer structure represents a package of a glass fabric and aluminum substrate. The structure is being exposed to a temperature field. It is necessary to find the temperature distribution field in the structure under study and determine the stressstrain state caused by the temperature impact. To determine the temperature field, an unsteady thermal conductivity problem for a fourlayer homogeneous rod is being solved. The assumption that deformation is being realized in a prismatic body of theoretically infinite length, loaded by the surface and voluminous forces normal to the zaxis, which intensity does not depend on z, is used for stressstrain state. It is assumed as well that the structure deforms as a whole entity, which corresponds to the Feucht model. Shear deformations are also absent. The article presents the graphs of the temperature field and heat flux distribution along the length of the package as a function of time. 
Eremin A. M. Conditions of optimality of classical ejectors in the frame of different theories of critical mode. Trudy MAI, 2023, no 130 In this article explores conditions for the optimality of a gas ejector in various theories of the critical mode. Explored three theories: Millionshikov—Ruabinkov theory, Vasiliev theory and Pearson, Holyday and Smith theory. System of equations of critical mode has been investigated on extremum by Lagrange method. New conditions of optimality have been obtained. For theories of Millionshikov—Ruabinkov and Pearson these condition for the optimality is blocking in pipe with flexible boundary and which corresponds to subsonic speed of gas in the place of blocking. New condition for the optimality for Vasiliev theory is equality of static pressures in mixed jets in the place of blocking. In the frame of each theory for a number of values of the reduced speed of active gas has been calculated values of compression ratio for k=0,1 and σ=10. Examination of these figures shows that in the case of classical condition of blocking λ_{2}=1 point with equal static pressures at the entrance of ejector responds to the maximum of compression ratio. In the case of blocking in the pipe with flexible boundaries point with equal static pressures at the entrance of ejector responds to the inflection point of compression ratio curve, but maximum of compression ratio responds to the sonic speed of gas in the entrance of ejector. In the frame of Vasiliev theory has been obtained that the case of equal static pressure in the place of blocking responds to the maximum of compression ratio and this case is different from critical mode. Also has been obtained that in frame of Pearson theory exists the condition of optimality, which differ from the condition of optimality by Vasiliev theory by the presence of an additional term. Although obtained condition is mathematically correct, calculations show that it can’t be realized in real ejector. 
Egorov I. A. Investigation of the flow characteristics of the arcuate wing. Trudy MAI, 2023, no 130 The article considers the lift coefficient determining specifics of the folding arcshaped wing determining. The effect of the wing arc curvature on the interference with the body is being estimated. The character of arcshaped wing lifting force dependence on the roll angle is being determined. Rational scheme of the arcshaped wing spreading is determined. The discrete vortices method is applied. The computation technique is presented in another article. Reference is available. A rectangular wing is being considered. Two options of the opening angle of 90° and 135° are regarded. The article demonstrates the possibility of the interference coefficient of the wing with the body determining by integrating the wing local angles of attack, and determining the average angle of attack. This is rather convenient for the wings of nonstandard configuration, including the arcshaped wing. A weak effect of arc curvature on the interference coefficient of the wing with the body is revealed. This is especially typical for the rational scheme arcshaped wing (with an opening angle of 135°). A significant specificity of the dependence of the lift coefficient of an arcshaped wing on the angle of roll is revealed compared to the similar dependence for a flat wing. It manifests itself most vividly for the arcshaped wing with the opening angle of 90°. This wing is of nonmonotonic character of the dependence of the lift coefficient on the roll angle with a minimum at the roll angle of 45°. The situation persists for the Xwing layout of the wings. An arcshaped wing with the opening angle of 135° has characteristics near to characteristics of a flat one. However, even in this case, the independence of the total lifting force from the roll angle for the Xwing layout of the wings is being not ensured. Conclusions:

Savin E. I., Minkov L. L. Research of drag coefficients and solid rocket motor parameters for the analysis of the movement of a shortrange bicaliber aircraft. Trudy MAI, 2023, no 130 A complex problem based on the determination of intraballistic and externalballistic parameters for evaluating the flight zone of a shortrange bicaliber aircraft is considered. The specifics of the shortrange bicaliber aircraft are shown. The solid rocket motor provides fast acceleration in a short time period to the required speed (active section). After the end of the active section the basic shell, which has a smaller caliber, is disconnected from the booster stage and continues to move in the energypassive section of the flight. This plan allows the use of solid fuel with high energy and temperature characteristics and the use of the lightweight composite materials design of the propulsion system. Also, resetting the booster stage of a larger caliber significantly improves the aerodynamic quality in the energypassive flight section. The law of change of the axial component of the thrust force in the quasistationary combustion duration of solid rocket motors is used for the thrust force mathematical description. Equations for the longitudinal motion of a material point in the atmosphere are used for the mathematical description of external ballistics. The dependence of the drag coefficient on speed and altitude is given. The Heunʼs method with a predictorcorrector scheme is used for the numerical solution of differential equations. The possibility of a preliminary evaluation of the flight zone with the coordinates of a shortrange aircraft is shown. To improve the accuracy of calculations, it is possible to supplement the systems of equations with components of the lateral force, lift force, Magnus force, aerodynamic moments, rudder angles, etc. Also, to improve the accuracy of the numerical solution of equations, higher order solution methods can be used. 
Baimetova E. S. Numerical simulation of hydrodynamic processes in a multichannel collector. Trudy MAI, 2023, no 130 Hydraulic device being considered in the article represents a component part of the heat exchanger, which includes distributing and receiving collectors. These collectors are interconnected by a set of eight parallel identical sections, located across the channels of the working fluid supply and discharge. Each section consists of six microchannels, which inner finning is accomplished in the form of symmetrical trapezoids with a narrow upper edge. The operative range of velocities for the given type of hydraulic device is 0.13 /s, and the flow within this operative range is laminar. The article presents modeling at the working fluid velocity of 0.1 m/s for two, four, six and eight sections of the collector according to the fundamental technique described in the I.E. Idelchik’s reference book on hydraulic resistances. Numerical modeling was performed with the openFoam package for solving continuum mechanics problems in the stationary setting based on finite volumes using the simpleFoam solver. Computations were made by the method of establishing using iteration convergence procedure by the velocity mistie of 10^{–7} and pressure mistie of 10^{–6}. The delivery collector computational grid was built in the Salome package and consists of 6 million tetrahedral elements for the eightsection collector. Analysis of the results obtained by the theoretical calculation of hydraulic resistances differs greatly from the numerical modeling data at the identical problem setting, which might be associated with poor applicability of the I.E. Idelchik’s technique for this kind of structures, and flagrant necessity for new techniques introduction for hydraulic resistance computing of complex collector systems. As the result of the study, the flow velocity distribution and pressure difference, decreasing with the number of sections increasing, were obtained as well, and the absence of hydraulic plugging along the equiscalar surfaces was demonstrated. 
Yan N. O. Oscillations of a stratified rotating fluid in a cylindrical cavity. Trudy MAI, 2023, no 130 In this paper, the problem of free oscillations of an ideal stratified rotating incompressible fluid filling a cylindrical cavity in a solid is considered. The normal oscillations of a stratified fluid at a low rotational speed are studied in the case of full or partial filling of a cylindrical round tank with liquid. Recently, there has been interest in the study of oscillations of a stratified fluid filling a vessel of finite dimensions (oscillations of oil and other liquids in various reservoirs). The study of the motion of a rotating ideal stratified fluid in a limited volume leads to very peculiar boundary and initial problems. In this paper, we investigate the problem of oscillations of an ideal incompressible stratified fluid whose density at rest varies along the vertical axis. The questions of the interaction of an ideal stratified fluid and the cavity of a moving solid body are considered, and solutions to problems of normal (natural) oscillations of a fluid with boundary conditions are presented. To study the vortex motion of a rotating homogeneous fluid, the method of state functions of S.L. Sobolev or the method of generalized potentials of F.L. Chernousko is usually used. The method of generalized potentials, which uses some restriction on the change of variables from time, is more convenient in this sense. The method of F.L. Chernousko makes it possible to emphasize the hydrodynamic problem from the general problem of the mechanics of the bodyliquid system in the most complete way. Numerical results of determining the eigenvalues and eigenfunctions of normal fluid oscillations are given at a constant buoyancy frequency in the form of tables and graphs. 
Kanashin I. V., Grigorieva F. L., Khromov A. I., Grigoriev Y. Y. Low cycle loading of a flat sample with a continuous displacement velocity field considering material compressibility condition . Trudy MAI, 2023, no 130 Low cycle loading of a flat specimen with a continuous displacement velocity field, taking into account the material compressibility condition. Subject of study — Determination of crack initiation moment conditions under lowcycle loading of a flat specimen with a continuous displacement velocity field under flat deformation and flat stressed state with consideration of material compressibility. The purpose of this work is to investigate the processes of tension, compression and sequential tensioncompression of a flat sample with a continuous field of displacement velocities under flat deformation and a flat stress state, taking into account the compressibility of the material at small deformations. The compressibility of the material associated with the law of conservation of mass, formulated in the form of the continuity equation, leads to a change in density in the process of loading, in accordance with which the logarithm of the material derivative of density over time is added to the system of equations determining the field of displacement velocities. The following methods were used in the study: analytical method for determining velocity and strain fields, propagating wave method for solving homogeneous differential equations. The following results were obtained in the course of the study:
The results of the study can be applied in the development of mathematical models of behavior of elements of real structures in the problems of modern mechanical engineering and construction, as well as in evaluating their strength. 
Win K. K., Temnov A. N. Variational formulation of nonlinear boundary value problems in the dynamics of two fluids performing a given motion in space. Trudy MAI, 2023, no 130 This article contains the derivation of the equations of motion of a solid case with a twolayer fluid, considered as one mechanical system. The dynamics is based on the principle of least action in the form of HamiltonOstrogradsky. The variational formulation of the problem of dynamics has certain advantages, for example, from the point of view of substantiating the necessity and sufficiency of the derived equations and boundary conditions, and considering the body and fluid as one system allows one to achieve a certain multiplicity. The mechanical meaning of the equations is interpreted, which are presented in several different forms, in particular, in the form of the Lagrange equations. The question of the integrals of the equations of motion and the conditions under which they take place is considered. The article is devoted to the formulation of the variational principle for a multilayer ideal heavy fluid located in a cylindrical cavity of a solid body that performs specified angular oscillations around a fixed axis. A similar problem is due to the fact that the application of the variational principle in continuum mechanics is based on the HamiltonOstrogradsky principle, the mathematical form of which is written in Euler variables for hydrodynamic problems acquires significant mathematical differences. The article shows that with the help of the variational principle, written in a form different from the traditional one, it is possible to obtain a complete set of equations of nonlinear motions of liquids, including nonlinear kinematic and dynamic conditions on the interfaces of liquids filling the cavity of a solid body that performs a given movement. 
Gumenyuk A. A., Marinina I. A., Shtrunova E. S. Development of a model of a laser triangulation rangefinder with a structured backlight. Trudy MAI, 2023, no 130 The article considers the problem of developing a laser triangulation rangefinder mathematical model with a structured backlight. Unlike the wellknown approach based on Bresenham algorithm application, the model enables subpixel accuracy of the centers forming of the backlight markers, as well as accounts for their shape and brightness distribution while the structured lighting projecting onto the object at various angles. Subpixel accuracy ensuring is achieved by determining the 3Dcoordinates of the highlight markers’ brightness peaks employing the ray tracing method, and their pixel coordinates by the projective camera model. Lambert’s law of cosines is used to compute the reflections intensity. The shape and angular orientation of the highlight marker image are being determined by information about the angle between the normal to the surface and the direction of the radiation incident on the object, as well as by the parameters variation of the twodimensional Gaussian distribution. 
Zvonarev V. V., Pitrin A. V., Popov A. S. Methodology for calculating the noise immunity of incoherent reception of signals with binary relative phase manipulation with linearly frequencymanipulated interference. Trudy MAI, 2023, no 130 To ensure the stability of information transmission using a radio channel, the influence of noise and interference is of great importance. In systems with relative (differential) phase manipulation (OFM), the socalled «reverse operation» mode is excluded. These signals are not much inferior in noise immunity to phasemanipulated signals. In addition, incoherent reception (demodulation) is possible, which greatly simplifies the receiving device. The use of such signals and incoherent reception is preferable in cases where the phase of the carrier oscillation changes dynamically and / or randomly and tracking it is difficult, especially in the presence of structural interference of various types. To calculate the probabilities of bit errors, we determine the models of the radio signal and interference. We derive formulas for calculating the average probabilities of bit errors of incoherent reception of a radio signal from OFM2 in the presence of linearly frequencymanipulated interference. The conclusion of the final formula for calculating the average probability of a bit error with a priori equal probability of information symbols is a halfsum of the probabilities of receiving the first (S1) and second (S2) bits. The graph of the dependence of the probability of a bit error on the signaltonoise ratio at fixed values of frequency deviation and interference levels shows at what level the signal is provided with the required values of the probability of a bit error. The graph of the dependence of the probability of a bit error on the magnitude of the frequency deviation is symmetrical with respect to its zero value. The curve in each direction has a wavelike appearance with decreasing minimum and maximum extreme values. Analyzing the obtained graphs, it can be noted that for certain, welldefined values of frequency deviation, the influence of interference with the LFM is minimal, and the less this influence is, the lower the level of interference. On the other hand, for some values of frequency deviation, the interference effect in the bit error probability metric is 34 orders of magnitude higher than the minimum values. The presence of interference leads to a dependence of the probability of a bit error on the value of the initial phases of both the signal and the interference, even in conditions of incoherent reception. To obtain a phaseaveraged value of the bit error probability, statistical averaging over the initial phases is necessary. The developed technique makes it possible to qualitatively or conditionally quantify the effects of linearly frequencymanipulated interference on the reliability of transmitted information in the radio channel when the interference frequency is shifted. 
Voznuk V. V., Kopalov Y. N. Investigation of the noise immunity of receiving OFDMsignals in the conditions of unintentional narrowband noise interference. Trudy MAI, 2023, no 130 The problem of estimating the noise immunity of OFDMsignal reception in the conditions of unintentional narrowband noise interference with different ratios of the width of the signal spectrum is considered. At the same time, narrowband noise interference is understood as Gaussian noise interference with a uniform frequency bandlimited spectrum, not exceeding the band signal frequencies. To solve this problem, a simulation model of the communication channel with OFDM has been developed. The simulation results are presented showing the change in the average probability of the channel bit and information bit errors depending on the spectrum width and the central frequency in the interference spectrum at different signaltonoise ratios. In the course of the study, the dependences of the average probability of a channel and information bit error on the signaltonoise ratio with a fixed signaltonoise ratio for OFDMQPSK type signals under the influence of a noise interference signal aimed at the width of the spectrum with different values of the central frequency in the interference spectrum were obtained. The dependences of the average probability of the channel and information bit error on the signaltonoise ratio with a fixed signaltonoise ratio for OFDMQPSK type signals under conditions of exposure to narrowband noise interference with different values of the spectrum width and a fixed central frequency in the interference spectrum were obtained. When developing the model, the theoretical foundations of OFDM signal generation technology were used, the proposed model implements cascade coding and interleaving similar to the IEEE 802.16 family of standards. It is shown that not only noise interference aimed at the width of the spectrum, but also interference with a spectrum width less than the width of the signal spectrum can have a negative impact on the noise immunity of receiving OFDM signals. 
Alrubei M. A. Comparative analysis of interpolation methods in evaluation of the frequency of a discretized harmonic signal. Trudy MAI, 2023, no 130 Accurate and efficient signal frequency measurement is an important signal processing task in many technical applications, such as radio electronics and communication systems, modern information transmission systems, research and medical, radio navigation and radar systems, monitoring of electronic equipment. Standalone frequency counters use discrete counting and interpolation methods, while embedded control systems employ spectral analysis methods using fast Fourier transform (FFT) with the largest spectral component determination and interpolation along two or three spectral lines. The article considers the effect of additive stationary noise on the estimate of a periodic signal frequency from the spectrum obtained by the direct Fourier transform application to an array of discrete samples, that is, during transition from the time domain to the frequency domain. Frequency estimation methods may be divided into the groups of signal representation in both time and frequency domains. Discrete counting and interpolation methods are most widely used in the time domain, as well as in the frequency spectral analysis using FFT algorithms for maximum spectral component determining and successive maximum coordinate correcting using mathematical transformations, such as interpolation. To reduce the effect of spectral leakage or spectrum deviation, time sequence smoothing is used through multiplying all signal samples by window function weights. The interpolation algorithms being used were modeled, and a modified formula that allows accuracy increasing of the frequency estimate by several fold was proposed. The interpolation method is the most widely used, indepth and most widespread correction method in the analysis of a discrete spectrum with error estimates depending on the number of samples and the number of spectral lines accounted for. In practical engineering applications, the most important indicators for the quality assessing of an algorithm are the ability to work in noise, speed, and low frequency estimation error. Based on a brief review of the state of theoretical research and development of interpolation methods for correcting the maximum sample position, the principles and characteristics of the interpolation algorithms currently used are presented. Characteristics of each algorithm are examined by simulation and interpolation errors are analyzed. 
Baburin A. A. Integer GLONASS phase ambiguity estimation methods. Trudy MAI, 2023, no 130 The article considers integer estimator methods for GLONASS phase ambiguities necessary in the problems of high accuracy absolute and relative positioning for GLONASS signals measurement with integer ambiguity resolution. Accounting for the integer properties of pseudophase ambiguities allows significant reduction in solution convergence time up to the centimeter accuracy level. With a view to frequency division of satellites signals, adopted for GLONASS signals, two problems arise while solving the problems highprecise positioning. They are the difference in the hardware delays of the receiver while measuring pseudodistances of various GLONASS satellites, and the difference between wavelengths of the signals carrier frequency of various GLONASS satellites. These specifics do not allow integer estimation of the GLONASS pseudophase ambiguities. Thus, the known methods developed for the systems with code division, such as GPS, cannot be employed for GLONASS. The presented article deals with the second said problem. Two methods of strict and nonstrict integer estimation based on solution of the uncertain system of the linear equations by the Stransform theory are being suggested. The strict integer method is based on integer unimodular transformto the system of linear equations prior to its solution, and does not require the presence of GLONASS satellites with neighboring characters in the visibility zone of the receiver. The nonstrict method is simpler in application, but integer estimations may be obtained only observing certain conditions. Conditions at which the difference from the integers may be neglected with the nonstrict estimation were analyzed. Both strict and nonstrict methods do not require engaging direct measurements of pseudodistances and pseudophases processing. Linear approximation of the receiver phasefrequency characteristic is being used for the pseudophase measurements model (linear dependence of the phase delays on the frequency in the receiver is being accepted). The analysis is being conducted on the example of the first differences of real navigation receivers of the IGS network processing, which confirms correctness of the suggested methods and adequacy of the mathematical models being used to the real measurements. 
Novikov A. N., Khorchev V. A. Calculation of the effective scattering surface of smallsized aerial objects. Trudy MAI, 2023, no 130 When synthesizing algorithms for detecting and recognizing smallsized aerial objects (SSAO), it becomes necessary to calculate their effective scattering surface (ESS). Smallsized aerial objects, such as light unmanned aerial vehicles (UAVs), UAVs with an electric motor, created according to the format of a flying wing, artisanal UAVs, etc. in recent years have become a threat that poses a danger to civilian and military facilities [1]. Considering that ESS is included in the radar range equation [2], its analytical calculation for the SSAO will allow determining the minimum range at which air objects can be detected by radio monitoring posts. As a result, the early detection of such aircraft will ensure the timely issuance of target designations to firing means for subsequent decisionmaking on the destruction of the SSAO. The article deals with the calculation of the RCS of simple objects and objects of complex shape. It has been established that the RCS of objects of complex shape, which include smallsized air objects, can be calculated analytically. The result of the article is a method for calculating the RCS of the SSAO, which involves the use of the RCS values of individual triangles obtained in the process of approximating the object under study in the modeling environment to calculate the resulting RCS. The article also presents the results of mathematical modeling obtained using the program «Altair Feko», backscattering diagrams of the UAV at different angles of incidence of an electromagnetic wave. As a result, it was found that the backscattering diagram will take maximum values at normal incidence of an electromagnetic wave, and decreases with a change in the angle of exposure of the object under study, respectively. 
Olkina D. S. Algorithm of semantic image segmentation for solving the problem of positionong an aircraft on the Earth`s surface. Trudy MAI, 2023, no 130 This work is devoted to one of the main methodological issues of using the objectoriented approach — choosing the method of segmentation of multichannel images. The methods for determining the approach to the development of a segmentation algorithm are considered, as well as the choice of distinctive features to solve the problem of segmentation of images of the earth’s surface to determine the coordinates of an unmanned aerial vehicle (UAV) in order to position it on the earth’s surface. The theoretical significance of the study is a numerical study of the formulation of the tasks of segmentation of images by stochastic methods. Of practical importance is obtaining the results of experiments on the segmentation of images of the visible and radio ranges, development of training tools and a software package that solves the problems of segmentation of multichannel images. The main objectives of the study are to develop a model of neural network segmentation of multichannel images of optical and radio range, сonstruction of the procedure for training segmentation models, obtaining comparative estimates of the computational complexity of algorithms and learning characteristics, hyperparametric optimization of various neural network models, obtaining the main dependencies of training parameters, quality and speed of models. The work uses the neural network of semantic segmentation Bisenet, which allows you to get segmented images of the earth’s surface in real time. For the neural network Bisenet, some hyperparameters were configured: the most suitable optimizer and the best strategy for reducing the learning speed were identified (learning rate). 
Dorozhko I. V., Musienko A. S., Sundiev D. S. Simulation model linking reliability indicators with indicators of test and functional control of technical systems. Trudy MAI, 2023, no 130 At present, various builtin and external control tools are widely used to ensure reliability and maintain technical availability of spacerocket technology. Models and interrelations allowing associating reliability and control indicators are necessary for the requirements substantiation to the control system characteristics in the technical design assignment with account for the given value of the object availability factor. The article proposes a simulation model allowing evaluate a complex reliability indicator of an object, namely the availability factor, with account for the control system indicators and characteristics. Unlike the wellknown models, differentiated control application, i.e. functional and test ones with different parameters, is being accounted for. Test control is characterized by high reliability, but, as a rule, it leads herewith to the downtime due to the fact that during the test control the object is not in use or is used limitedly extent and some time is required to transfer it from the control mode to the operating one. Functional control is less reliable, but is being performed in the «background» mode, and downtime can be associated only with erroneous control results. The developed model accounts for these types of control specifics. The admission on the parameters stationarity is eliminated as well. The developed model allows processing timevarying values of mean time between failures to account for various intensity of the technical system use for its intended purpose, as well as storage modes. As the result of the simulation modeling, the availability factor values and the graphs of the availability function were obtained and analyzed. The inference was drawn that, if necessary, the availability function may be used to establish a boundary, below which the value of technical availability should not degrade throughout the entire time. The practical significance lies in the possibility of employing the proposed model to adjust the frequency of the existing technical objects control, as well as to justify the requirements for control systems in the technical specifications formation for the development (modernization) of automated control systems and technological equipment for the spacerocket technology. 
AbdAli L. M., AlMaliki M. N., Kuvshinov V. V., Kuznetsov P. N., Morozova N. V. Mathematical technique modeling using the algorithm for control of the maximum power point for a photoelectric system. Trudy MAI, 2023, no 130 Substantial number of solar electric power generating systems, including those associated with aerospace technology, is being employed to ensure various equipment operation. These systems are being applied on space stations and offline groundbased facilities, for power supplying for stationary operating complexes, as well as for supplying energy to various industries and consumers. One of the basic elements of a solar photovoltaic station is automatic system of its power characteristics control. The presented article studied the point of maximum power control system for the offline power generating installation based on silicon photoelectric panels. One of this work tasks consisted in operation reliability enhancing of the solar system because of the climatic factors affecting it and associate this system operation with the typical requirement of electric energy through the artificial intelligence application. As long as the alternative renewal energy forms are based on natural resources permanently replenished, it is assumed that they are of infinite storage of useful power. The proposed arithmetic model being is an important component of the complex study of photoelectric systems. The proposed arithmetic model is an important component of the comprehensive study of photoelectric systems. The programming environment, which includes numerous models for renewable energy systems, allows analyzing photoelectric installation operation regularities. It is possible to build a plurality of models for the renewable energy systems meant for modeling and analyzing photoelectric installations operation with MATLAB/Simulink. Due to the instability of external factors, such as solar radiation and atmospheric temperature, or unpredictability of possible instances, such as solar panels overheating, it is necessary to employ a maximum power point tracking (MPPT) algorithm for the systems of semiconductor photo converters. The proposed control algorithm application allows significant efficiency increase of the energy converted by the solar station of electric energy, as well as reliability enhancing of the main and auxiliary equipment of photoelectric systems, which may be employed for supplying the offline objects and operation for the energy system. 
Nguyen N. D., Doan T. T., Nguyen T. T., Tran Q. M., Nguyen Q. A., Ngo V. T. Landing trajectory optimization and simulation for miniUAV considering constraint of control and landing speed. Trudy MAI, 2023, no 130 This article presents the method of optimizing the landing trajectory of miniUAV considering constraint of control and landing speed and the method of tracking the found trajectory. The chosen controls are namely normal and tangential overload. The selected objective function is in the Bolza form, including landing accuracy and energy consumption during flight. Applying the Pontryagin’s maximum principle turns the optimal control problem into the boundary problem, which is solved by the parameter continuation method. To verify the optimal trajectory being gained, the authors selects a specific type of UAV to simulate tracking on the aforementioned trajectory through the Matlab Simulink software. The results show the application of the optimal trajectory tracking controller assures the accuracy and safety of UAV landing. 
Gumbatov D. A. Analysis of the adequacy of gammacorrection of the shading effect in spectral surveys of the earth's surface using unmanned aerial vehicles. Trudy MAI, 2023, no 130 The effect of shading in the real scene under study should be taken into account when studying the state of vegetation using various vegetation indices. For example, the values of such widely used indices as NDVI and LAI are slightly higher in sunny areas compared to shaded areas. The shading effect can also provide useful information of a geometric nature about the location of remotely studied objects in the environment. The object of the study is the effect of shading during spectral surveys of the earth using UAVs equipped with spectral cameras. The subject of the study is the adequacy of the gammacorrection of the shading effect, carried out during spectral surveys. The purpose of the study is to study the degree of adequacy of the gamma correction method for objects that are partially shaded. A significant difference is shown in the degree of adequacy of the γcorrection as applied to objects of the same type with an identical degree of shading in the case of applying the methods of geometric and algebraic averaging. The average value of DN can generally be calculated in two ways: 1. Geometric averaging method. 2. Method of algebraic (convolutional) averaging The difference found is that in the case of geometric averaging, the adequacy of the γ correction is understood in the sense of equality of the average value of the logarithm of the corrected value of the geometric averaging of the shaded and unshaded parts of objects to the average value of the logarithm DN for the unshaded part. However, in the case of algebraic averaging, the adequacy of γ correction is understood in the sense of equality of the average value of the logarithm DN of the unshaded part to the average value of the logarithm of the γcorrected value DN of the shaded part of objects. 
Kasatikov N. N., Fadeeva A. D., Brekhov O. M. Multiagent system for monitoring objects of the energy complex. Trudy MAI, 2023, no 130 The purpose of the presented article consists in developing a multiagent system capable of effective management and control of various objects of a power complex. The system will employ artificial intelligence (AI) and machine learning (ML) techniques to analyze data from sensors and other sources to detect and prevent potential problems, optimize energy consumption and improve overall efficiency. The multiagent system will enable communication and cooperation between the various agents involved in the management of the energy complex, such as operators, engineers and maintenance personnel, as well. The final goal of the article consists in creation of the system, capable of reducing the dead time, enhancing productivity and increasing safety in the energy complex. The work is of a review character, about multi agent system of a «smart city» and its application at the energetics and spacerocket industry in the first place. The results of this work are proposed steps on the multiagent system general development for its implementation at the power and spacerocket enterprises. The article describes how the «smart city» multiagent system may be applied at the spacerocket enterprises and power objects in various ways. These systems may be helpful while controlling complex and interrelated processes, associated with space missions, form the spacecraft start and to its operation. Multiagent systems may enable connection and coordination between different agent, such as groundbased control and satellite systems. They may as well be helpful in energy consumption optimizing and reduce the number of waste due to the energy consumption and storing control. Besides, these systems may help with the maintenance service, revealing potential problems prior they become critical, as well as increasing the space mission overall security and effectiveness. The multiagent system application at the power objects and spacerocket enterprises may present several advantages such as efficiency, reliability and cost effectiveness enhancing. One inference that can be drawn consists in the fact that the multiagent system would help optimizing energy production and consumption by coordination and control of the separate agents’ behavior. Each agent in the system may have its certain functions such as energy consumption monitoring, equipment operation control or decision making on the energy storage and distribution. One more inference consists in the fact that the multiagent system is able to increase the energetics objects reliability by ensuring redundancy and fault tolerance. In case of one of the agents’ failure, other agents will be able to keep on running and compensate the failure, reducing the risk of dead time and increasing the overall reliability of the system. Besides, the multiagent system may increase economic efficiency by the energy losses reduction based on the real time data. The system may help as well to control the energy demand reducing peak loads and demand for the extra power for energy production, which will result in savings on costs for both energy suppliers and consumers. As a whole, the multiagent system employing on the spacerocket objects and power objects would lead to significant increase in energy efficiency, reliability and economic efficiency, which makes it an upandcoming approach to control and optimization of power systems. 
Abdurashidov T. O., But A. B., Chupina E. S. Results of numerical simulation of the supersonic jet. Trudy MAI, 2023, no 130 The paper presents calculations of supersonic cold turbulent jets using the application software. The calculation results are compared with experimental data. Methods are given for adapting the computational grid to obtain highquality calculation results and save machine resources in the course of calculations. Computational studies of the outflow of supersonic jets, along with experimental works [1, 2, 5–13, 20], are of practical importance for engineering design work in the field of launch vehicle design and their operation. One of the main stages of numerical modeling is the validation of mathematical models on small experimental setups, which should confirm the correctness of the chosen mathematical model and methods for solving the numerical problem. Validation of the outflow of hot gas at supersonic speeds is complicated by the special nature of the flows, which have shock waves in their structure, the complex chemical composition of combustion products and possible chemical reactions that determine the characteristics of the flow. In this paper, we consider the issue of numerical simulation of the shock wave structure described in the literature [1–4] and the turbulent flow of a cold supersonic jet, and also compare the calculated values with experimental data. The calculations presented in the article showed that the use of local adaptation of the grid in the regions of gradients made it possible to reduce the cost of computing power by 8.6 times, and also to achieve good agreement between the numerical results and the results obtained experimentally on a supersonic experimental model. 
Gadzhiev M. M., Kuleshov A. S. Stability of steady motions of a body with a fixed point in a flow of particles. Trudy MAI, 2023, no 129 The problem of motion of a rigid body with a fixed point in a free molecular flow of particles is considered. Suppose the flow consists of identical non — interacting particles, moving with constant velocity along a fixed direction in a fixed absolute space. Suppose the particles interact absolutely inelastically with the rigid body, i.e. after collision the velocity of a particle with respect to the rigid body is zero. Suppose the surface of the rigid body is strictly convex. Then, under assumption, that the flow velocity considerably exceeds the product of the characteristic value of the angular velocity of the rigid body and the characteristic distance from the rigid body to a fixed point, the explicit expression for the moment, acting on the rigid body with a fixed point from the flow of particles are obtained. It is shown, that equations of motion of the rigid body with a fixed point in a free molecular flow of particles are similar in many aspects to the classical system of equations of motion of a heavy rigid body with a fixed point. The corresponding equations of motion of the rigid body with a fixed point in a free molecular flow of particles have partial solutions for which the rigid body performs permanent rotations with constant angular velocity around the streamlines of the flow. Necessary conditions of stability of these permanent rotations are obtained by analyzing the linearized system. When the rigid body is dynamically symmetric, the necessary and sufficient stability conditions of the corresponding steady motions are obtained by analyzing the effective potential of the system. 
Popov I. P. Free sinusoidal oscillations based on the mutual exchange of kinetic energy between three loads. Trudy MAI, 2023, no 129 It is noted that free sinusoidal oscillations in a classical mechanical oscillator are stipulated by the mutual transformation of kinetic energy into potential energy. The oscillator, in which free sinusoidal oscillations are being accompanied by the transformation of the kinetic energy of an inert element into the same kinetic energy of another inert element is wellknown. The elements with another nature of reactivity are missing in such oscillator. Such oscillator is essentially monoreactive. This oscillator disadvantage consists in its imbalance due to the asymmetry of the structure, which may require additional vibration protection measures. This drawback can be avoided by applying a symmetrical scheme with three weights. For the purposes of this work, it is convenient to employ a flat threecoordinate system similar to the threephase coordinate system used in electrical engineering. For an arbitrary vector R, lying in the threecoordinate plane, which origin coincides with the origin, Theorem 1 is true. The coordinates x_{1}, x_{2}, x_{3} of the vector R form a regular triangle, which size does not change with an arbitrary rotation of the vector R. Theorem 2. The middle of the vector R is aligned with the center of the triangle x_{1}x_{2}x_{3}. Half of the vector x_{1}x_{2}x_{3} plays the role of a crank, which in real devices is needed to develop the angular velocity ω and communicate the moment of force to compensate for dissipative losses. In a monoreactive harmonic oscillator with three weights, free sinusoidal oscillations of any given frequency may occur, which is determined solely by the initial conditions. 
Pismarov A. V. To the question of prediction of the endurance limit of threaded parts with surface hardening. Trudy MAI, 2023, no 129 A review of the literature was carried out in order to study the state of the problem of predicting the endurance limit of threaded parts. Smooth parts and parts with stress concentrators are considered. An analysis of the destruction of threaded parts (bolts, studs, etc.) experiencing alternating loads during operation shows that, in general, the destruction of threaded parts is of a fatigue nature. The influence of surface hardening of threaded parts by methods of surface plastic deformation has been studied: to increase the service life, that is, to increase the life cycle during the operation of threaded parts at the stage of their manufacture, surface hardening methods are widely used. The maximum effect of their application is achieved under conditions of stress concentration. This is justified, since the destruction occurs in places where the prismatic geometry is violated. It has been established that surface hardening leads to the appearance of compressive residual stresses in the surface layer, which increase the endurance limit of threaded parts. Methods for predicting the endurance limit of threaded parts are considered, their accuracy and reliability are assessed. A separate block considers the issues of modeling the stressstrain state of a loaded threaded part in order to determine the endurance limit by numerical methods. At the stage of machine design, it is important to be able to evaluate the effect of the applied methods of surface plastic deformation. Based on the review, it is concluded that it is necessary to develop a method for predicting the fatigue limit of hardened threaded parts, taking into account manufacturing technology, tightening forces, operating conditions and other factors. 
Balunov K. A., Solyaev Y. O., Golubkin K. S. Application of the topological optimization method for the structural synthesis of a stiffeners in a kink zone of a high aspect ratio wing. Trudy MAI, 2023, no 129 The article considers an approach to the reinforced thinwalled structures design based on the topological optimization method application for models of variable thickness shells. The authors regard the problem of the optimal structural scheme selection of stiffeners in the kink zone of a high aspect ratio wing. The authors regard the problem on the structureforce scheme selection in the fracture zone of the highaspectratio wing. The article contains the optimization problem formulation and computational results for the three variants of the wingtip sweep angle with the specified loading in the form of distributed aerodynamic pressure and concentrated forces at the points of the wing mechanization elements fixing. Numerical modeling is being performed with the models of MindlinReissner type shells, which thickness is being determined by the values of the additional node variable, being introduced in the topological optimization problem. Optimal thicknesses distribution along the model elements at the specified limitations on the structure weight and stiffening fins height is being defined by the results of the optimization problem solution with the goal function in the form of the total energy of deformations, occurring in the solution. The solution regularization is being ensured by the minimum size selection of the finite element mesh elements. The article demonstrates that the applied technique and topological optimization results may be employed for optimal framing set configuration of reinforced thinwalled structures with enhanced weight effectiveness. 
Bykova T. V., Mogilevich L. I., Evdokimova E. V., Popova E. V., Popova M. V. Simulation of strain waves evolution in the walls of coaxial annular and circular channels filled with viscous fluid and made from incompressible material with fractional physical nonlinearity. Trudy MAI, 2023, no 129 The article being presented develops approaches to mathematical modeling of nonlinear strain waves propagation in the continuous heterogeneous media. These models are uptodate and scientifically significant for the prospective aerospace engineering due to the moreandmore increasing application of modern composite materials with significantly nonlinear physical and mechanical properties. The authors proposed a mathematical model for circular and annular channels completely filled with viscous fluids and formed by the two coaxial cylindrical shells. The shell material is considered incompressible and possessing the physical law with fractional degree nonlinearity, associating stresses, strains and strain intensity. Derivation of equations of the shell with fractional nonlinearity dynamics (Schamel nonlinearity) was performed to develop a model. The coupled hydroelasticity problem for the two coaxial cylindrical shells filled with viscous fluids was formulated. The fluid dynamics were considered within the framework of the Newtonian incompressible fluid model. Fluid motion in annular and circular channels is being studied as creeping one. The authors performed an asymptotic analysis of the hydroelasticity problem, and obtained a system of two nonlinear evolution equations generalizing the Schamel equation. It was demonstrated theoretically that in the considered statement, the presence of a viscous fluid in a circular channel has no effect on the nonlinear wave process in the shellwalls of the channel. The article proposes a new difference scheme for solving the obtained system of the two nonlinear equations based on application of the Grebner bases technique has been proposed. A series of computational experiments have been carried out, which revealed that the nonlinear strain waves in the walls of the considered channels are solitons. 
Dobryshkin A. Y., Sysoev O. E., Sysoev E. O., Petrov V. V., Bormotin K. S. Investigation of the frequency characteristics of the motion of a thinwalled cylindrical shell with a low added mass taking into account torsional vibrations. Trudy MAI, 2023, no 129 The destruction of shell structures is a rare manmade disaster that occurs for numerous reasons. When designing shelltype structures, calculations are made for strength and stability, operating modes are taken into account, and real calculations are not made for the occurrence of the resonance phenomenon, which thinwalled shell structures are subject to. This happens due to the discrepancy between the existing mathematical models and the behavior of real structures. To combat the phenomenon of resonance, designers usually increase the safety margins when calculating shells, which increases the cost of objects, but does not completely solve the problem. In most cases, this resonance phenomenon is combated by strengthening the structures, which leads to an increase in the material consumption and cost of the structures. Antiresonant devices are used extremely rarely, despite their low cost, since the available mathematical models do not accurately describe the process of vibrations of cylindrical shells. And without accurate mathematical models, it is impossible to control antiresonance devices. In this paper, the authors refined the computational model of the process of vibrations of a shell of small length (ring) carrying a small added mass, taking into account torsional vibrations, and experimentally verified the model obtained. The study is a consideration of the contour, which in this case can be represented as a cylindrical shell of small length (ring). Quite logical is the criterion of the oscillatory motion of this shell, namely, changes in the radius in the course of vibrations. Based on the data obtained, it can be concluded that the vibrations of the shell, in this case, radial and torsional vibrations predominate, are classified as highfrequency vibrations. 
Kyaw Y. K., Rabinsky L. N. Evaluating the effectiveness of the method of topological optimization of reinforced panels based on analytical solutions to benchmark problems. Trudy MAI, 2023, no 129 This article regards a variant of the problem of a flat freely supported plate loaded with a concentrated force applied at a displacement relative to the center of the plate and acting along the normal to its surface. For such a problem, the topological optimization technique formulated earlier by the authors for the models of plates of variable thickness offers a simple solution for selecting the optimal orientation of stiffening ribs that ensures minimum deflections of the plate under load. In the topological optimization problem, the resulting stiffening ribs are arranged symmetrically relative to the plate central plane, and the angle between them depends on the magnitude of the load application point displacement. To check the efficiency of the applied optimization technique the authors suggested considering a similar problem for a planespace frame, in which the element structure repeats the arrangement of the stiffness ribs that appear in the solution of the topological optimization problem for the plate. The solution for the frame deformation problem can be easily constructed in analytical closed form. It is possible to determine the optimum angle of opening of the frame elements for a given location of the load application point based on this solution. The article demonstrates that there is a qualitative consistency between the optimal geometry of the frame found from the analytical solution and the optimal geometry of the corresponding reinforced plate found from the solution of the topological optimization problem. Particularly, the same characteristic dependence of the optimal angle of stiffening ribs opening on the magnitude of load application point displacement relative to the center of the plate is established. 
Thant Z. H. Interaction of a plane pressure wave with a spherical shell in an elastic medium. Trudy MAI, 2023, no 129 This article considers the nonstationary problem of a plane pressure wave impact on a spherical shell in an elastic medium. Both desired and prescribed functions are represented in the form of series by the Lejandre and Hegenbauer polynomials to obtain the analytical solution of the nonstationary diffraction problem of the flat pressure wave on the spherical surface in an elastic medium supported by the thin shell. The solution method is based on the expansion into series on the system of eigenfunctions and application of the Laplace integral transformation in time. As the result, analytical expressions were obtained for all desired functions, which allows studying nonstationary strainstress state and displacements both on the shell and at any point of the elastic medium. The problems of elastic waves diffraction on various types of heterogeneities relate to the most difficult and uptodate problems in the dynamics of deformable bodies. In the applied terms, it is explained by the circumstance that the information on the stressstrain state near these irregularities is of great interest for various purposes. Besides, the presence of heterogeneities (inclusions, cavities, notches, local changes in properties, etc.) is an indispensable condition arising in various fields of modern engineering. Such tasks include the following: creation of new structures, working at dynamic loads, development of new composite materials and their introduction at creation of engineering constructions, modern tasks of geophysics and seismology, and also a number of other tasks of scientific and technical character. 
Cherkasova M. V. Simulation of thermal and erosion processes in a multichannel hollow cathode. Trudy MAI, 2023, no 129 The article is devoted to the study and modeling of work processes in a multichannel hollow cathode. A similar cathode design is used in various plasma devices and highcurrent electric rocket engines. The design is relevant for use in electron closeddrift engines or ion engines currently being developed worldwide for use in powerful transport space systems. The article presents the theoretical foundations of twodimensional modeling of thermal, electrical and erosion processes in a multichannel packed hollow cathode operating in an arc mode with pumping of plasmaforming gas. The formulated system of equations allows calculating the local and integral characteristics of the cathode based on the minimum possible set of input parameters. Distribution of cathode temperature, current densities in cathode body and plasma channels, plasmaforming gas pressure in channels, concentration of charged and neutral particles are simulated. Also described is a model of erosion processes, which includes processes of evaporation, sputtering, recycling, which makes it possible to calculate local and integral erosion of the cathode. The article also presents the results of an experimental study of several samples of multichannel cathodes and compares the results of the experiment and design modeling for a number of key parameters: cathode temperature and cathode voltage drop depending on the consumption of plasmaforming gas and discharge current. An important point is the comparison of the results of cathode erosion. The model predicts the voltagecurrent dependencies and the erosion rate within the 10% of accuracy, while the temperature calculation is affected by an error of about 20%. The results show that the proposed model correctly describes the parameters of the cathode and can be used in the design of this type of cathodes. 
Kaurov P. V. Calculation of the flow of a viscous fluid near an inlet and outlet. Trudy MAI, 2023, no 129 The article considered and solved the problem on the viscous fluid flow between the source and the drain at small Reynolds numbers. It presents the analytical solution of the Stocks equation when bipolar coordinates utilization. The soughtafter function is represented as a sum of the two components, first of which satisfies the boundary conditions, while the application of the other component satisfies the initial Stocks equation in the bipolar system of coordinates. Approximation of the first component the flow function by the simple dependence allows reducing the initial equation with variable coefficients to the three ordinary differential expressions with constant coefficients relative to the second component of the flow function. Analytical solution is presented for the three ordinary differential equations. The examples of the computed flow function in the dimensionless form for various distances between the source and the drain are presented. Comparison of the flow functions calculated values with the experimental data from the literature sources demonstrates reasonable agreement. 
Usachov A. E., Isayev S. A., Sapunov O. A., Usachov S. A. Optimization of the flow around thick airfoils to improve their aerodynamic characteristics. Trudy MAI, 2023, no 129 The problem of optimizing aerodynamic thick airfoils is relevant for the development of nontraditional aircraft, such as a flying wing [1], a hybrid airship [2], etc. Modern numerical simulation methods make it possible to optimize the aerodynamic airfoil shape according to a given objective function. In this study, the task was to reduce the aerodynamic drag of the airfoil with its largest area, that is, in the threedimensional case of maintaining maximum internal volumes. The commercial ANSYS software package (license number 501024) was used for optimization. Numerical modeling of the airfoil flow was carried out on the basis of solving the complete NavierStokes equations, averaged over Reynolds (RANS—ReynoldsAveragedNavierStokes) and closed using Menter’s twoparameter SST turbulence model. The shape of the profile is changed by varying a number of geometric parameters on the upper surface of the profile. Half of a circular cylinder with rounded sharp edges was chosen as the initial profile shape. By optimizing the profile shape using numerical simulation methods, its aerodynamic quality has been significantly increased. Numerical simulation of a twodimensional turbulent airfoil flow was carried out using the Fluent CFD software package included in the ANSYS computing environment. The Fluent package contains a fairly wide range of tools for numerical simulation of turbulent flows, however, based on the experience of previous studies [3,4,11] and known literature [1120], the main methods for calculating the turbulent flow around a profile were determined. The control volume method was used to discretize differential equations [3,4,11,20]. Using the semiimplicit SIMPLE method [20], the pressure was determined, the secondorder upwind scheme QUICK was used to approximate the flow terms on the edge of the control volume, and the secondorder upwind scheme was used for the turbulence parameters. Based on previous studies [35], the flow around a thick airfoil with a separation zone has been improved by using vortex cells. The application of the vortex cell method is based on the placement of ovalshaped cavities in the area of the separation point from the upper surface of the profile, in which a circulation flow is organized in one way or another. 
Temnov A. N., Shkapov P. M., Yu Z. . Mechanical model of lowviscosity liquid sloshing with capillary effects. Trudy MAI, 2023, no 129 The author derived a boundary condition considering energy dissipation near the threephase contact line based on the Hamilton—Ostrogradsky principle. A numerical algorithm has been developed for calculating the damping factor due to energy dissipation near the threephase contact line based on the finite element method. A variation formulation of the problem is derived from the of the motion equations linearization of the liquid relative to the equilibrium free surface. The area occupied by the fluid was discretized by the finite elements, and the eigenvalue problem, which solution represented a complex frequency, was obtained. In the work being presented, a pendulum and a spiral spring simulate the impact of mass forces and surface tension force respectfully, and the fluid viscosity is accounted for by the linear damper. The mechanical analog parameters are determined from the principle of dynamic similarity, eigen frequency, damping factor and kinetic energy of the fluid and its mechanical model. The article presents quantitative estimation of the capillary number Ca (viscous force and surface tension force interrelation), the Bond number B0 (mass forces and surface tension force interrelation) and the liquid filling factor β (liquid volume to the vessel concavity ratio) effect on the damping factor and eigen frequency of the capillary liquid oscillations. It follows from the studies that the capillarity number greatly affects the energy dissipation near the threephase contact, and its value in the range of 10–100 leads to the greater value of the damping factor of the order of the damping coefficient on the vessel wall. The obtained results may be employed for the dynamics and stability studies of the rooster super stages, upperstage rocketsand other spacecraft with the liquid containing cavities. 
Biryukov I. D. Development of an optimal algorithm for processing radio signals of radio emission sources by aviation radio surveillance tool. Trudy MAI, 2023, no 129 This paper presents the process of developing an optimal algorithm for processing radio signals from sources of radio emission by an aviation system of radio technical surveillance. The main tasks of radio signal processing, which are solved by aviation means of radio technical surveillance, are described. The interdependence of the decisions made in the detection, resolution, estimation of parameters and recognition of radio signals from sources of radio emission is shown. An analysis of the factors that reduce the effectiveness of radio surveillance equipment is carried out, and ways to improve it are proposed. For the case when the source of radio emission belongs to the a priori type library, the procedure for performing processing tasks is substantiated. The loss function is defined, which describes the process of processing information about the received radio signals and provides the interconnection of the decisions made. Based on Bayesian synthesis, an algorithm has been developed in which the problem of a priori uncertainty is solved by changing the sequence of performing radio signal processing procedures. A block diagram of the developed algorithm is presented. The feasibility of the developed algorithm is assessed. The relevance of the work on the development of an algorithm for processing radio signals in aviation system of radio surveillance is due to the complexity of the modern electronic environment, the increasing importance of objects containing radio emission sources, and the need for effective countermeasures. The joint optimal algorithm provides the lowest total Bayesian risk, but is not feasible due to high computational costs. Therefore, it is required to make a transition to a joint quasioptimal algorithm. 
Korol D. G., Temchenko V. S. Study of a cylindrical conformal antenna array with a patch emitter for UAV. Trudy MAI, 2023, no 129 The article proposes an approach that makes it possible to place a scanning antenna array with a patch emitter on an unmanned aerial vehicle without reducing its aerodynamic characteristics. The purpose of this work is to research the characteristics of conformal antennas on a cylindrical surface, which allow wideangle scanning at the required frequency and polarization for further use in unmanned aerial vehicles. The object of research is antenna arrays modeled in the CST Microwave Studio program, placed on a cylindrical surface. The result of the work is to obtain the necessary phase distribution and the excitation sector of the antenna array elements to achieve the required field of view during scanning. The approximation of individual sections of the aircraft by simple geometric figures such as a cylinder, a ball and a cone was adopted. They decided to place the antenna array on the fuselage, which was presented as a cylinder. The phase distribution is found using the geometrical optics approximation to focus the beam in a given direction. Azimuth scanning takes into account the shape of the cylindrical surface. To reduce the level of spurious radiation without using the amplitude distribution, we have selected the optimal excitation sector of the antenna array elements. The simulation results confirmed the possibility of scanning the antenna array in a given sector of angles in azimuth and elevation. The proposed approach for creating an antenna array can be built into an unmanned aerial vehicle, after the design has been finalized, already taking into account the real device. It will also be necessary to design the feeding system with phase shifters, power splitters and antenna switches. 
Alrubei M. A., Pozdnyakov A. D. Frequency estimate for symmetric and asymmetric structure of spectral components of sampled harmonic signal. Trudy MAI, 2023, no 129 A sampled harmonic signal frequency estimating is an important task while signal processing in many applications such as radio communications, monitoring and control systems and others. Discrete spectra may be employed to measure frequencies of the sine signal components. The said measurement consists in digitizing the composite signal, performing window processing of the signal samples and cpmputing their discrete amplitude spectrum, usually using a fast Fourier transform algorithm. However, the frequency of a sine component can be determined with improved resolution using the moment method of the largest consecutive element of the spectrum corresponding to this component. The abscissa of its maximum represents the best frequency approximation. An algorithm for the frequency estimating of a sampled harmonic signal of limited duration by the method of moments is proposed, which allows obtaining a weighted average estimate of the energy spectrum peak position. The methodological component of the error depends on the degree of closeness of the frequency true value and the energy center position, due to the type of window function. The error is being determined by the step of the fast Fourier transform (FFT) frequency grid, the type of the window function used, and duration of the signal sampling interval. The article shows a noticeable effect of the even and odd structure of the spectral lines being accounted for. In the symmetry region of the even spectrum structure, when the levels of the principal components change, a jump in the methodological error is formed, which can be eliminated by introducing correction or limiting the operating frequency range to the region of odd symmetry. The authors propose introducing an estimate of the spectrum structure into the algorithm and automatically select an even number of spectral lines for the spectrum close to even symmetry and an odd number for odd symmetry to compute frequency. The maximum methodological error can be reduced herewith by an order of magnitude or more. Some windows allow increasing the frequency measurement resolution by more than an order of magnitude. The purpose of this article is to show as well that even better results are achieved using the Chebyshev window. This method has been employed to set up measurement systems in control and management systems. 
Parshutkin A. V., Buchinsky D. I., Komlyk D. A. Investigation of noise immunity of signal receivers with discrete phase modulation in the conditions of interference with angular modulation and noise. Trudy MAI, 2023, no 129 The article deals with the noise immunity study of the coherent quadrature receivers employing signals with discrete phase modulation, and considers the impact of an additive mixture of white Gaussian noise and anglemodulated unintentional interference during the BPSK and QPSK signals reception. Spectrum bandwidth of the interference with angular modulation and its center frequency match spectrum bandwidth and center frequency of the useful signal. The bit error rate was used as quality indicator of the receiver’s functioning. The article presents an analytical study of the bit error rate dependence on the ratio of the useful signal power to the powers affecting the receiver of unintentional noise with angular modulation and white Gaussian noise. The association of the obtained expressions with the known expressions describing the effect of separately white Gaussian noise and unintentional interference with angular modulation on a coherent signal receiver with discrete phase modulation is adduced. The article explains how these expressions may be obtained from those obtained, by way of the passage to the limit. The authors demonstrate with the obtained expressions that at the certain powers of unintentional interference significant change of the bit error rate dependence on the signalnoise ratio is possible. The obtained analytical dependences of the bit error rate while receiving both BPSK and QPSK signal against the background of unintentional interference and white Gaussian noise may be applied to assess the electromagnetic compatibility of communication systems using discrete phase modulation signals. 
Tyapkin P. S. Hardwaresoftware complex for approvement methods of blind signal processing in radio systems. Trudy MAI, 2023, no 129 This paper presents the results of the development of a hardwaresoftware complex for testing blind signal processing methods in problem of increasing noise immunity in communication systems. The developed hardware and software complex includes two mixing circuits, a multichannel receiver and a personal computer. Digital receiver is based on the combination of softwaredefined radio systems (SDR) and consists of eight analogtodigital converters, a fieldprogrammable gate array (FPGA) circuit and a PCIExpress bus for transmitting data to a PC for processing and demodulation. The description and functional setting of the purpose of receiving and processing signals are involved in the work, as well as the results of verification of the hardwaresoftware complex. The results of verification of practical methods for the use of blind signal processing capabilities for interference in radio information transmission systems are obtained. When checking, the maximum data transfer rate in the continuous bit stream mode was determined when processing a mixture of BPSK signals with pulse noise of various shapes. This transmission rate exceeds 905 bps. To increase the maximum speed, it is possible to use a more powerful PC, transfer the demodulator and blind signal processing algorithms to the FPGA. 
Podstrigaev A. S. Assessment of the complexity level of the signal environment for the use of a multichannel subNyquist receiver. Trudy MAI, 2023, no 129 The modern cognitive radio systems and the spectrum monitoring devices used in spectrum management must perform wideband signal analysis. One of the ways to achieve a wide instantaneous analysis band is to use a multichannel subNyquist receiver. Such a device receives signals from the many Nyquist zones and analyzes their aliases in the first zone. It can disambiguate frequency measurements by aggregating information from several independent channels having different sampling frequencies. Previously, the author studied errors in determining the timefrequency parameters of pulses timeoverlapped in the subNyquist receiver prototype. These studies have shown that this receiver can be used in a complex signal environment. At the same time, the assessment of the maximum level of the signal environment complexity, at which it is possible to use a subNyquist receiver, has yet to be previously performed. This estimation is carried out in the present work by determining the number of pulses simultaneously processed with a given quality. As a quality criterion, we assume the probability of correct classification should be no worse than 0.8. For this, the abnormal error probability in determining the timefrequency parameters of the pulse should be no more than 0.1. A numerical experiment showed that this condition is satisfied when the number of pulses overlapped in time is not more than 4...5 (depending on the parameters of the receiver). The calculation shows the possibility of transmitting a stream of pulse descriptor words over the 10GE interface, assuming that five pulse descriptor words are formed in each analysis window (the worst situation). The bandwidth of the transmission channel is more than six times. In accordance with the previously considered classification of the signal environment, the receiver under study can be used in a signal environment of the third level of complexity and lower. The results can be used to substantiate the composition of wideband analysis tools depending on the expected complexity level, select the parameters of a multichannel subNyquist receiver, and predict the appearance of abnormal errors in determining the timefrequency parameters of pulses in the receiver. 
Sychev M. I., Osipov P. V. The radar tracking based on multiple model approach. Trudy MAI, 2023, no 129 As of today, the onrush development of the unmanned aviation and of its application scope are observed. Besides the application in economic activity, the scope of the unmanned aviation functions by special services and in military sphere is constantly growing. The smallsized and nearly invisible unmanned aerial vehicles present are of special peril. The problem of lowobservable targets detecting, tracking and intercepting for the socially significant objects protecting occurs. The article proposes a method for integration of the unmanned aviation detection, tracking and intercepting managing means, as well as synchronization of the control for these tasks solving. The article presents the description of the open information transfer protocol used in a wireless twoway exchange channel for the interception means control. Classes of possible interception objects and the structure of the complex for the interception process organization are determined. The article proposes scenarios of interception options, and presents their time characteristics as well as describes the options for radar stations that ensure detection of smallsized and lowobservable objects with low values of the effective scattering area. The article describes the currently uptodate task of identifying features of the aerial objects observed by radar for recognition and decisionmaking with the allocation of classes of artificial and natural origin as well. The article defines methods of useful data extracting from the reflected signals employing a convolutional neural network, and considers two options of neural network structuring, in which the input data is represented as a graphical representation of the spectrum of the reflected signal (in grayscale) and in the form of arrays of numbers. 
Maksimov S. A., Naumchenko V. P., Ilyushin P. A., Pikunov D. G., Solovyov A. V. Strapdown inertial measurement unit shock absorption and damping linear system analysis. Trudy MAI, 2023, no 129 The presented article considers the result of the dynamic system synthesis describing the amortization and damping system behavior of the strapdown inertial measurement unit for a spacecraft. The "JSC "TsENKI"—"NII PM" Inhouse design highaccuracy vibrationstring accelerometers are employed in the unit as sensitive elements. With account for the internal shock absorption system, these accelerometers may be described as oscillating links with small damping coefficient and finite free movement, which limits their application with external vibrational highenergy impacts. The necessity of extra shock absorbing system introduction to the unit is being dictated by the device readings utilization in the spacecraft control system in all flight modes, including offnominal ones. This shock absorbing system is also an oscillatory link affecting the shock absorbing system in the accelerometer, and subjected to the response impact from it. As the result, the problem resolves itself into developing a system with the feedbacks encircling oscillatory links with its subsequent analysis. Linear acceleration in the form of a random signal comes to the system input, and the system output is a linear translation, which is necessary to be kept within certain limits. The JSC "TsENKI"—"NII PM" has the experience in the dynamic system prototype unit resistant to the external mechanical impacts developing. The article considers the process of design, development and analysis of the linear model of the shock absorbing and damping system described in Python language and confirmed the possibility of ensuring the given requirements to the unit sturdiness to the input impacts. As the result, the optimum range of dynamic characteristics of the damping and shock absorbing system was found. The obtained results will be used further for the nonlinear system modeling and its indepth analysis. 
Sentsov A. A., Polyakov V. B., Ivanov S. A., Pomozova T. G. Method of interception of small and inconspicuous unmanned aerial vehicles. Trudy MAI, 2023, no 129 As of today, the onrush development of the unmanned aviation and of its application scope are observed. Besides the application in economic activity, the scope of the unmanned aviation functions by special services and in military sphere is constantly growing. The smallsized and nearly invisible unmanned aerial vehicles present are of special peril. The problem of lowobservable targets detecting, tracking and intercepting for the socially significant objects protecting occurs. The article proposes a method for integration of the unmanned aviation detection, tracking and intercepting managing means, as well as synchronization of the control for these tasks solving. The article presents the description of the open information transfer protocol used in a wireless twoway exchange channel for the interception means control. Classes of possible interception objects and the structure of the complex for the interception process organization are determined. The article proposes scenarios of interception options, and presents their time characteristics as well as describes the options for radar stations that ensure detection of smallsized and lowobservable objects with low values of the effective scattering area. The article describes the currently uptodate task of identifying features of the aerial objects observed by radar for recognition and decisionmaking with the allocation of classes of artificial and natural origin as well. The article defines methods of useful data extracting from the reflected signals employing a convolutional neural network, and considers two options of neural network structuring, in which the input data is represented as a graphical representation of the spectrum of the reflected signal (in grayscale) and in the form of arrays of numbers. 
Gumbatov D. A. Optimization of a multicycle remote sensing system using UAVS. Trudy MAI, 2023, no 129 The subject of the study is multicycle remote sensing systems, particularly, the optimal multicycle remote sensing systems based on unmanned aerial vehicles (UAVs). Analysis and synthesis of a multicycle remote sensing mode is being realized by measuring equipment installed on the UAV. Two optimization problems are considered and solved. In the first problem, measurement cycles in the number of n differ in the fact that the flight altitude in every cycle is different, and the problem of determining the optimal relationship between the flight altitude and the cycle duration is being set. The second optimization problem envisages computing the optimal dependence of the cycle duration on the length of the distance traveled during one cycle. As the result of solving the first problem, the author shows that a specially formed functional of the target, called the «UAV flight area», will reach its minimum if the flight altitude is decreasing so far as the duration of the measurement cycle is increasing. The result of the second problem solution reveals the amount of information obtained in multicycle mode reaches its maximum value given a direct interrelation between the said indicators. The results obtained in this work may be applied while the development and application of remote sensing systems, based on the unmanned aerial vehicles, operating in a multicycle mode. The main inference of the study consists in the fact that remote sensing systems operating in multicycle mode may be optimized by various criteria. The optimization criterion selection herewith depends on the purpose set for the concrete realization of the remote sensing system based on the UAV. 
Stepanov A. R., Pavlov P. V., Vladimirov A. P. Hardware and software complex speckle laser diagnostics of aircraft cabin glazing elements. Trudy MAI, 2023, no 129 The article presents the results of the research oriented to developing a method and device for technical condition determining of the aircraft cabins glazing elements. Technical ways of constructing an optoelectronic nondestructive testing system capable of determining the amount of movement of aircraft glazing elements during changes in excess pressure inside the cabin of the aircraft are considered. The authors propose employing the speckle structures method of optical radiation, which operating principle is based on determining the glazing elements displacement by the parameters changing analysis of the speckle fields being recorded, as a nondestructive control tool. The rigging for installing and sensing the glazed parts of the aircraft cabin with the speckle field was developed for practical realization of the said method. The program module for the speckle fields being registered recording and processing with subsequent issuing the amount of the controlled cabin glazing section displacement at the excessive pressure occurrence in the cabin was developed as well. The article presents the results of the fullscale tests of the pilot sample of the developed hardwaresoftware complex while the aircraft cabin tightness determining by analyzing the changes in the number of cases of glazing escaping from the sealing. The test results confirmed the claimed possibility of determining the size of the glazing escape from the sealing with the developed hardware and software complex. Application the complex during the of aviation equipment operation will significantly reduce economic costs and the number of errors in determining the size of the glazing escape from the sealing s well as increase the probability of determining the of the adhesive joint destruction inside the sealing. 
AbdAli L. M., Yakimovich B. A., Syaktereva V. V., Kuvshinov V. V., Morozova N. V. Optimization of the automatic control system for the maximum power point for a windsolar generating plant with energy storage. Trudy MAI, 2023, no 129 Direct solar energy conversion systems based on semiconductor photovoltaic cells have been employed for decades for aerospace technology and groundbased consumers. The article presents the developed information and control system for combined electric energy generating installation by solar and wind energy conversion. A combined system, which employs two or more stable energy sources, is known as a hybrid renewable energy system. It will facilitate uninterruptible energy generation and allow employing one source in the absence of the other, which is its irrefutable advantage. The study proposes the hybrid energy conversion positioning, which includes photovoltaic panels, wind power generator and batteries. The presented work performed control system optimization of the proposed hybrid windsolar system, which enhanced significantly efficiency of its application and performance reliability. The model of photovoltaic and wind output power, as well as the model of the battery charging and discharging were obtained by studying the output characteristics of the generating power station. Parameters such as the average annual net profit as a target function and region and area characteristics, planned scale, complementary properties, resources utilization factor and stability of the output as limitations were used while development. A model for the hybrid system of photovoltaic conversion, wind generation and energy storage was constructed employing the proposed method. The results of the experiment demonstrate the proposed approach validity and robustness. The emissions trading revenues inclusion makes the model more accurate. The ideal result is more useful as well. As the article shows, the solar photovoltaic panels distribution affects the overall power generation of the hybrid system. It employs a solar panel connected with a hybrid controller and a wind turbine. The results revealed that continuous power generation was possible when the solar panel was connected with the wind turbine, which improved its power output. 
Kuznetsov Y. L. Design and ballistic analysis of the prospects of using a singlemodule launch vehicle to supply an orbital station in a sunsynchronous orbit. Trudy MAI, 2023, no 129 This article is concerned with the substantiation of the design appearance of a reusable singlemodule launch vehicle (LV), which ensures the delivery of a playful payload (PlP) on board the orbital station. The design appearance of the LV is determined by the totality of its geometric, mass and energy characteristics. During the research, the KORONA singlemodule LV project designed at the OAO “Makeyev Rocket Design Bureau” was used as a parent variant. The research included a comparative analysis of the schemes of the power plant (PoP) and the layout of fuel containers for the LV, which ensures the delivery of the PlP to the orbital station operating in a sunsynchronous orbit with a height of 350 km and an inclination of 97 degrees. When determining the massdimensional characteristics of the LV, it was assumed that a PlP with a total mass of 5000 kg was delivered to the orbital station, which includes a cabin with a crew of four and 2000 kg of cargo in an unpressurized compartment, followed by the recovery of the crew and 200 kg of associated cargo to earth. Calculations of energy characteristics were carried out by modeling the motion of center of mass of the LV during the development of a typical flight pattern. This pattern includes launching the LV into an elliptical exchange orbit, ballistic pause, testing of the apogee pulse, which ensures the transfer of the LV to the working orbit of the station, splicing, deorbiting by testing the deceleration pulse, aerodynamic deceleration in the atmosphere and the final rocketdynamic braking, which ensures a soft landing of the LV near the launch point. According to the results of the research, the design appearance was formed and the limit (critical) masses of the structure and fuel filling were determined, as well as the PoP parameters of the reusable singlemodule LV of the KORONA type, which will ensure the delivery of the PlP of a given mass. It is shown that for the universal LV used in the transportation of manned and unmanned PlP, as well as to increase the mass perfection of the design of the LV, it is advisable to produce oxidizer and fuel tanks in the form of a monoblock with combined bottoms, and place the PlP in the front of the LV. A rational scheme of PoP operation is substantiated, which provides for a single activation of a cryogenic main engine with a central body used to form a transition orbit with an apogee height equal to the height of the station's working orbit, with the development of subsequent pulses using an orbital maneuvering engine (OME) of limited power on highboiling fuel components. It is shown that the parameters of the OME: thrust and the geometric degree of nozzle expansion should be optimized from the condition of ensuring a minimum fuel consumption in the area of prelanding braking. A high sensitivity of the mass of the PlP derived by a singlemodule LV from the height of the working orbit was revealed, which is due to a significant excess of the final mass of the LV structure compared to the mass of the output PlP. This feature limits the scope of application of a singlemodule reusable LV to circular orbits with a height of no more than 350400 km. 
Chernikov A. A. Algorithm for detecting and classification of objects on a unhomogeneous background for optoelectronic systems. Trudy MAI, 2023, no 129 This article discusses the automatic detection and classification of unmanned aerial vehicles (UAV) and armored vehicles (BT) in the optical flow for optoelectronic systems. The algorithm is able to detect and classify objects in real time against a nonuniform background. Despite the presence of a fairly large number of methods for detecting and localizing objects in images, the solution of this problem to the full extent is still a rather laborious task, which, as a rule, requires manual labor of expert operators, which requires large time costs and may affect the efficiency of detection. The purpose of the presented work is to increase the efficiency of detecting complex objects of interest against the background for further classification of objects. When detecting the probable location of the object, the twodimensional wavelet transform algorithm and the DBSCAN spatial clustering algorithm were used. A convolutional neural network was trained to classify the detected object. When training a convolutional neural network, a training sample was prepared, consisting of real and simulated images of objects. The algorithm for automatic detection and classification of objects was developed in Python using the OpenCV library. At the end of the work, the results of an experimental study of the developed algorithm are presented, on simulated and real images in the infrared range. The presented studies were performed using video image processing methods for object detection and a convolutional neural network for object classification. The proposed algorithm can be used to detect objects against an inhomogeneous background in real time by optoelectronic system in the infrared range. 
Popov I. P. On the speed of approach of objects during space flights. Trudy MAI, 2023, no 128 _{}It is noted that the first feature of the speed of approach of objects is that it can exceed the speed of light c, in contrast to any relative speed. We consider an inertial frame of reference with three recorders located in coordinates x_{0}=0, x_{1}, x_{2}. Recorder clocks are synchronized. At the moment of time t_{0}, the registrar located at the coordinate x_{0 }registers the passage of the first object, and the registrar located at the coordinate x_{2} registers the passage of the second object. At the moment of time t_{1}, the registrar located in the coordinate x_{1 }registers the passage of both objects. The speeds of objects are constant. In the reference systems associated with the first and second objects, no measurements are made. To calculate the speed of approach of objects in this situation, the only way of reasoning is possible, namely: at the moment of time t_{0}, the distance from the first object to the second was ^{0}l=x_{2}–x_{0}; at the moment of time t1this distance became equal to zero; so the approach time was ^{0}τ=t_{1}–t_{0}; therefore, the speed of approach of objects is equal to the ratio of these quantities. At the Large Hadron Collider, the speed of protons approaching is almost twice the speed of light. The aim of the work is to establish other features of the speed of collinear approach of two objects. The rate of collinear approach of two objects in relativistic mechanics is an essentially ambiguous quantity The results obtained do not contradict anything, do not refute anything, and are not a paradox. 
Kuleshov A. S. On the reduction of some systems of classical mechanics to the Liouvillian form. Trudy MAI, 2023, no 128 In 1846, J. Liouville indicated a class of holonomic mechanical systems for which the Hamilton — Jacobi equation can be integrated by the method of separation of variables. Mechanical systems belonging to this class are called Liouvillian systems. In the case of two degrees of freedom, it is known, that the Liouvillian system admits, in addition to the energy integral, another first integral, quadratic in generalized velocities. The presence of two first integrals for a holonomic mechanical system with two degrees of freedom allows us to assert that such a system is integrable. Moreover, it is possible to study the bifurcations of the joint levels of the first integrals. The corresponding method for Liouvillian systems with two degrees of freedom was developed by Ya. V. Tatarinov and V. M. Alekseev. To use this method, it is necessary to reduce the studied mechanical system to the Liouvillian form. The paper considers several wellknown systems of classical mechanics (the Euler — Poinsot case of the problem of the motion of a rigid body about a fixed point, the Jacobi problem of geodesics on an ellipsoid, the problem of motion of the Chaplygin sphere on the perfectly rough horizontal plane), which, by changing variables, take the form of Liouvillian systems with two degrees of freedom. Moreover, to reduce the problem of rolling motion of the Chaplygin sphere to the Liouvillian system, the theory of Chaplygin reducing multiplier is used. Previously this approach was not used in solving the Chaplygin sphere rolling problem. As a result, the study of the dynamics of the considered systems can be carried out using the methods of the theory of topological analysis with the separation of variables according to Liouville. 
Borshevetskiy S. A. Determining the location of additional supports of a pivotally supported plate under harmonic loading. Trudy MAI, 2023, no 128 The article proposes a method for determining the location of such additional supports for two models of plate movement: Kirchhoff and Timoshenko. A rectangular thin pivotally supported plate of known dimensions of constant thickness, which has additional supports in area, is considered. Additional supports installed with the same pitch along the coordinate axes, forming equal segments. The harmonic concentrated force acts on a random place of the plate. It is necessary to determine the location of additional supports based on the stiffness condition: the maximum deflection does not exceed the set value. To determine the location of a set of supports, the segment size satisfying the stiffness condition is first determined. The solution soughting using the influence function, as a reaction of the system to a single impact. Since the harmonic load is representable by Euler, the problem reducing to a stationary one. Additional supports replaced by compensating loads. The influence function decomposing into double Fourier series satisfying the hinge support at the edges. Unknown reactions in the supports are determined from a system of linear algebraic equations according to Kramer’s rule. Then everything substituting into the condition of structural rigidity and this equation solving. At the end of the article, a numerical example and verification calculation giving, which show the fulfillment of the structural rigidity condition. The main advantage of the proposed methodology is the analytical form of the solution. This allows you to substitute any characteristics of the material, the geometry of the plate, as well as the magnitude of the desired load. In general, the technique is also applicable for shells using a local coordinate system that allows the shell to expand into a plate. 
Dobryshkin A. Y., Lozovsky I. V., Sysoev O. E., Sysoev E. O. Study of vibrations of a cylindrical shell with added mass with consideration of contour extension. Trudy MAI, 2023, no 128 As of today, the commodities turnover role increase in the global economy is an objective factor. The role of aerial delivery vehicles and outwards the Earth increasing requires the quality improvement of flying vehicles, which basis is formed by the shells. The shells demonstrate indisputable advantages, namely strength, tightness and streamlining over the other options of structural schemes. In operation, these shells are being subjected to various loadings, such as wind load, varying atmospheric pressure, temperature loads, and loads of engineering systems for human life support. For this reason, light and strong structural materials are used for these shells manufacturing. One of the most commonly used materials is aluminum. It has a number of advantages such as low density at significant strength, durability, resistance to many types of impacts. Due to the limited choice of material for the aircraft production, researchers are searching for other options to improve the structures strength and reliability. For example, the study of internal mechanisms of movement or refinement of the computational model. As an example, there is the problem of the forced and natural oscillations presence in the open thinwalled cylindrical shells, which arise due to the cyclic or quasistatic external effects. Frequencies overlapping of both natural and forced vibrations may lead to unacceptable amplitudes of the structure oscillatory process, which will lead to these shells destruction. As of today, the oscillatory behavior analysis of the structure in the design of aircraft structures is not being performed due to their relatively small size, as well as the lack of appropriate techniques and analytical models. Thus, it is necessary to study various aspects of structural vibrations and, in particular, the effect of the added mass on the frequency characteristics of the oscillatory process of thinwalled cylindrical shells. 
Eliseev A. V., Kuznetsov N. K., Mironov A. S. Maps of dynamic invariants in the estimation of modes of motion of mechanical oscillatory systems. Trudy MAI, 2023, no 128 The scientific and methodological foundations for the dynamics problems solving of technological and transport facilities operating under conditions of increased vibrational dynamic loads are being developed. The purpose of the proposed research consists in developing methodological approaches for the assessment, control, formation and management of dynamic states of technical objects (machines, equipment, working bodies of vibrating technological machines), which design schemes of are being displayed in the form of mechanical oscillatory systems with several degrees of freedom. The studies are based on employing and developing analytical apparatus of system analysis and its applications to the problems of machine dynamics, protection of equipment and devices from vibration effects, which forms the basis of approaches to ensuring safety, reliability of operation of technical means, ensuring the dynamic quality of technological machines. The article considered the issues of the development of ideas on the generalized states of mechanical oscillatory systems formed by solids under conditions of coherent vibrational loads of a forceful nature, which dynamic state of is being determined based on the dynamic malleability of points distributed over the surface. The authors suggest considering the socalled dynamic invariant, reflecting the essential features of the mechanical oscillating system dynamic states aggregate in the form of oriented graphs, as a generalized dynamic state. The number of its of vertices and arcs are equal to the number of resonances, frequencies of amplitudes zeroing , as well as positive and negative forms of the elements dynamic interactions. The article shows that an infinite set of amplitudefrequency characteristics can be juxtaposed with a finite set of dynamic invariants. The general aggregate of dynamic invariants can be constructed based on the zeroing frequency functions, which can be set implicitly by zeroing the transfer function numerator, interpreted as dynamic compliance within the framework of the problem under consideration. The zeroing frequency unction juxtaposes the frequency of external force disturbances with the variation parameters of the system, on which the dynamic compliance is being zeroed, assuming that the zeroing frequency does not coincide with the natural oscillation frequency of the system. The article demonstrates that the aggregate of dynamic states corresponding to the simultaneous variation of two system parameters may be displayed by the dynamic invariants chart, splitting the plane of two variation parameters into the finite aggregate of nonintersecting areas, boundaries and planes with potentially different dynamic variables. It shows, in particular, that infinite diversity of dynamic states of mechanical oscillations may be represented in the form of finite set of generalized dynamic states. 
Temnov A. N., Yan N. O. Rotation around a fixed point of a solid body with an ellipsoidal cavity completely filled with an inhomogeneous fluid . Trudy MAI, 2023, no 128 In this paper, the equations of spherical motion of a solid body with a rotating inhomogeneous incompressible fluid filling a completely ellipsoidal cavity are obtained and investigated. The stability of rotation of a solid with an inhomogeneous fluid having a linear density distribution is considered. The purpose of this article is to study the effect of an inhomogeneous fluid on the stability of rotation of a solid with a fluid around the axis of dynamic symmetry. In the formulation of the problem, a solid body with an ellipsoidal cavity rotates at an angular velocity around a fixed point that coincides with the geometric center of the cavity, and an inhomogeneous ideal fluid completely filling this cavity performs a homogeneous vortex motion in it with the angular velocity of the fluid. To derive the equation of motion of the system under consideration, we use the EulerLagrange equations, which, under the action of potential forces. To solve the problem of the stability of the system’s motion, we use the second Lyapunov method, and construct the Lyapunov function using the Chetaev method. Sufficient conditions for the stability of the rotation of a solid body with a fluid around the vertical axis of dynamic symmetry are derived. The condition is obtained in the form of inequalities of the roots of quadratic forms corresponding to the perturbed motion of a body with a fluid. The obtained equations of motion make it possible to study the stability of stationary motions of the system in question in order to assess the effect of fluid stratification on the dynamics of the body. 
Khatuntseva O. N. On the «determinization» of stochastic processes with increasing degrees of freedom in the system. Trudy MAI, 2023, no 128 The issue of the origin and existence of nondeterministic, i.e. stochastic processes in various physical, biological, social and other systems is an extremely complex and interesting task. Despite the longstanding interest in them on the part of scientists, there are still discussions on whether «stochasticity» is the true antipode of «determinism», or it reflects only a certain degree of our ignorance about the system or process under study. These problems are being conjugated, in particular, with the issues on predetermination of the various systems dynamics and the Universe as a whole. After the new branches of science emergence in the last century and, quantum mechanics, in particular, many issues related to the «stochasticity» have lost their urgency, since the concept of «uncertainty» has become fixed at the microlevel as one of the fundamental scientific concepts. However, the issue of the uncertainty «loss» while transition from micro to macro systems remains an open scientific problem. The article raises questions on the fundamental possibility of the stochastic process emergence in the systems described by the deterministic autonomous differential equations obeying Cauchy’s theorem on existence and uniqueness, as well as questions related to the possibility of «determinization» of stochastic systems with the number of degrees of freedom increase. The author shows that not only deterministic chaos with a structure difficult to analyze and interpret in the systems of autonomous differential equations, but true nondeterminism, i.e.«stochasticity» may occur stipulated by the incompatibility of differential equations due to the finiteness of the time step. This phenomenon may occur herewith at any arbitrarily small, but finite step in time. The author managed to demonstrate the work that that an increase in the degrees of freedom in the system under consideration leads to its «determinization». This phenomenon allows, in particular, answering the question on why stochastic systems with a large number of degrees of freedom, such as, developed turbulent fluid flows, large star clusters (such as galaxies), etc., are quite deterministic on average and demonstrate a stable dynamic state. 
Kotel'nikov V. A., Kotelnikov M. V., Krylov S. S. Mathematical modeling of injection of negative ion flux into the wall plasma. Trudy MAI, 2023, no 128 To solve the problem of radio communication with hypersonic aircraft, it is proposed to create a radiotransparent channel by injecting a stream of negatively charged ions into the boundary layer. The negative volume charge arising inside the channel primarily displaces lighter negatively charged particles — electrons — from it. The electron concentration decreases, which leads to a weakening of the attenuation of radio waves and radio communication is restored. The positively and negatively charged ions remaining in the channel due to their relatively large mass do not affect the passage of electromagnetic waves. A computer simulation of the injection of a negative ion flux into a dense plasma has been carried out. In the process of solving the task, the following stages can be distinguished:
The mathematical model of the problem at the first stage, taking into account the weak degree of ionization, splits into two independent systems of differential equations for neutral and charged particles. The electrodynamic part of the problem, taking into account the assumptions made at the first stage, includes the continuity equations for ions and electrons and the Poisson equation for a selfconsistent electric field. The method of sequential iterations over time was used to solve the problem. In this case, the perturbed zone evolves from the initial to the final stationary state. The latter is considered as the desired solution to the problem. The continuity equations for ions and electrons were solved by the Davydov method of large particles, and the Poisson equation by spectral methods in which the desired function decomposes according to the eigenfunctions of the differential operator. At the second stage, the emission of a stream of negatively charged ions into the space formed at stage 1 begins. The mathematical model of the second stage includes the equation of motion of negative ions, the continuity equations for all charged components and the Poisson equation for a selfconsistent electric field. The continuity equations were solved by the Davydov method of large particles, the equation of motion of negative ions — by the arithmetic mean method, the Poisson equation — by spectral methods. The evolution of ion and electron currents on the probe (stage 3) was traced to their establishment. The distribution of potential, electron concentration and concentration of negative ions along the beam axis, the values of the current density of positive ions and electrons on the disk from which the injection occurs were investigated. 
Poyarkov I. V., Lipatova L. I. Experimental methods for recording the process of diffusion instability in gas systems. Trudy MAI, 2023, no 128 The article provides an overview of experimental methods for gas mixture registering the transition from a stable diffusion mode to a state of diffusion instability while mixing process. Experiments on mixing process registration of gas systems by the shadowgrams method are described. This method allows observing the mixing process dynamics, determining visually the boundary of the mode change during the mass transfer process, as well as obtaining qualitative information on the spatial nonuniformities distribution and the nature of their behavior throughout the unstable mixing process. The catarometric method allows recording the mixing process dynamics, starting from the irregular fluctuations in the total concentration and ending with a steady convective process. The article provides the description of quantitative methods for determining the system thermodynamic parameters, at which diffusion instability occurs. The method for thermodynamic parameters determining with respect to the partial flows of the mixture components allows accurate computing of the stable diffusion boundary, and the method of criteria numbers application allows obtaining the value of the critical number of convective stability for a multicomponent gas mixture under isothermal conditions in the gravity field. The pros and contras of employing the methods in the article while the system parameters determining, at which transition from the diffusion region to the region of unstable diffusion occurs, are analyzed. It is noted that experimental methods — the tenegram method and the catarometric method — allow us to observe the nature of the mixing process, while quantitative methods — the method of determining thermodynamic parameters with respect to the partial flows of the mixture components and the method of using criterion numbers — allow us to find the conditions under which it changes. 
Azarov A. v., Latyshev A. E., Rozhkov S. S., Semernin M. A., Slavyansky A. O., Karavaev M. N. Experimental methods for recording the process of diffusion instability in gas systems. Trudy MAI, 2023, no 128 The paper considers and substantiates the options for constructing a highspeed radio communication line based on an active phased array antenna (APAA) with electronic beam scanning. The methods of beam scanning, power distribution systems and schemes for supplying power to the emitting elements of an active phased array are considered, namely, a circuit with a series supply of APAA emitters is considered, a circuit with a series supply of APAA emitters based on phase shifters is considered, a circuit of parallel supply of APAA emitters is considered, as well as a binarylevel scheme of parallel power supply of emitters of an active phased array. Requirements have been produced for the key element for supplying power to APAA emitters — annular resistive power divider, a block diagram of the APAA transmitter (beamforming module) has been proposed, including an antenna array, each emitter of which is connected to the corresponding transmitter module, which are powered through power distribution devices, signals conversion path, signal generation and processing devices, control device. While working on the requirements produced, the structure of annular resistive power divider was developed, which has a standing wave ratio of the input and output voltage of no more than 1.05 in the frequency band of interest, an isolation between the output channels of the divider of at least 27 dB, and a phase nonidentity of the outputs of no more than 0.2°, which meets high requirements for the accuracy and speed of electronic scanning by the APAA beam of the onboard equipment of highspeed radio links for use in radio communication systems of advanced spacecraft. 
Buzhin I. G., Antonova V. M., Mironov Y. B., Gaifutdinov E. A. Load balancing algorithm for service traffic in the virtualized infrastructure of next generation mobile networks. Trudy MAI, 2023, no 128 One of the key features that distinguishes future generation mobile networks (5G and 6G) from the previous generations is an increase in the number of services provided, a significant increase in data transmission speeds and a highly reliable control loop. The architecture of such networks is being built employing Software Defined Networking (SDN) and Network Functions Virtualization (NFV) technologies, as well as Network Slicing technology. It is necessary to develop messages load balancing algorithm of the virtualized infrastructure between the control devices to ensure the high fault tolerance level of control, load balancing, network connexity of mobile network architecture of future generation mobile network by the SDN/NFV technology employing. All SDN switches should be necessarily divided into the groups depending on their output loading so that the common loading from one group of switches does not exceed the SDN controller productive capacity for the load distribution (PacketIn messages received by the controller per second) from the virtualized infrastructure based on the SDN/NFV controllers. This requires permanent load measuring on each of the controllers. The main challenge is the loadbalancing task, i.e. the SDN switches allocation over controllers. The network topology can be plotted as a graph, where the nodes represent the SDN switches (virtualized infrastructure nodes) with the rated load about network states and the controllers with the rated data flow processing capacity, while the graph edges represent the data links. Let us decompose the task into two subtasks; each of them herewith is being solved by a different algorithm. The first algorithm has to divide the switches into groups based on the information on the current loads and flows in the system, so that the groups can be assigned to the controllers employed in the system. The second algorithm should allocate the groups resulting from the first algorithm running to the employed controllers so that the minimum number of migrations would be required to convert the considered system. The algorithm for PacketIn messages allocating to controllers is new and has no equivalents for comparison. The algorithm results in groups of virtualized infrastructure nodes with the total service traffic load not exceeding the maximum performance of the control loop nodes. 
Volkov A. S. The development of simulation model of channel with burst error arrays. Trudy MAI, 2023, no 128 The article studied one of the most uptodate problems in telecommunications associated with the bursterror channels. Thus, the model of a discrete channel in communication system under the bursterror arrays based on Gilbert model was developed. The burst error affects critically the received signal reliability under conditions of Gaussian noise and in some cases fully distorts the received signal. The purpose of the article consists in considering the main properties of the Gilbert channel and their impact on the data sequence transmitted through wireless communication channel under conditions of the additive white Gaussian noise (AWGN). The valuation function of the main variables in Gilbert channel is the probability scheme N = ⟨P,Q,E⟩, which includes the purposive parameters being described by this model: P is a probability of a “good” channel state, Q is a probability of a “bad” state, while E stands for the probability of error in the “bad” channel state. Thus, the article proposes the adaptive generation algorithm of bursterror arrays according to the said parameters of the probability scheme. Simulation model of the communication system by the Gilbert model and AWGN was developed. An extra block, allowing the code word supplementing with zeroes was described for it. This backup block was introduced for the further studies with a view to additional energy gain. One of the most important topics we touched upon is matrices interleaver and deinterleaver. In the end of the article, we adduce the simulation results with the advantage of about 3dB from this algorithm application. Besides, the bursterror correction procedure by the nonbinary ReedSolomon encoder/decoder with various schemes in the discrete communication channel is being considered. Conclusion of the article gives the simulated method assessment with plots and comments on the bit errors probability dependence on the Es/N0, its disalignment range, as well as analysis of the matrix interleaver depth. A system communication model including the Gilbert channel in conjunction with the AWGN is proposed. This work allows assessing the effectiveness of solutions on the package error control under conditions of Gaussian noise. 
Tyapkin P. S., Vazhenin N. A. Increasing the noise immunity of communication systems under conditions of pulsed quasiharmonic interference using blind signal processing methods. Trudy MAI, 2023, no 128 In this paper, to compensate impulse noise, we consider the use of blind signal separation methods. Blind methods are based on highorder statistics and operate under multichannel reception conditions. Currently, this direction is being actively researched and implemented in medicine and image processing. A simulation model of a digital radio information transmission system was developed. The purpose of simulation modeling was to study blind signal separation algorithms to compensate for impulse noise, as well as to analyze the effect of Gaussian noise on the quality of blind separation. Blind source separation algorithms have some limitations, such as: number of received sources must be more than number of signals, which must be statistically independent between themselves. As a result of simulation modeling, it was revealed that the use of blind signal processing methods in the fight against pulsed quasiharmonic interference makes it possible to achieve an energy gain depending on the duty cycle of the pulsed interference, the normalized interference frequency detuning relative to the bandwidth, the bit signaltonoise ratio and the interferencesignal ratio. For example, when demodulating a BPSK signal in a mixture with pulsed quasiharmonic noise, a duty cycle of 0.005 and an interferencetosignal ratio of 15 dB, the use of the SOBI (Secondorder blind identification) blind source separation algorithm makes it possible to achieve an energy gain with respect to mixture demodulation without blind separation at bit signaltonoise ratio of 8.1 dB or more. So, for example, with the same simulation parameters, with a bit signaltonoise ratio of 13 dB, a gain in bit error probability is achieved by more than в 2‧10^{3} times. 
Korovin A. V., Savin D. I. Тhe method for determining the coordinates of ground objects by an unmanned aerial vehicle using a laser rangefinder. Trudy MAI, 2023, no 128 The article proposes a method for the ground objects coordinates determining from an unmanned aerial vehicle, which allows increasing the accuracy of of the ground objects location determining. The aircraft is supposed to fly in a circle with the ground object observation until the achieved value of the spatial geometric factor is less than three. The accuracy increase occurs through the observation time increase for the object being explored, and accumulation of measured by the laser rangefinder ranges to it. The unmanned aerial vehicle absolute proper coordinates are assumed known in each moment of range measuring. Estimates of the carrier absolute coordinates were obtained with the navigation equipment of the global satellite navigation systems consumers. This approach will allow determining coordinates in hardtoreach and impassable terrain with high accuracy when solving various tasks. The unmanned aerial vehicle is being equipped with navigation equipment of global navigation satellite systems consumers being a source of navigation information. The carrier is also equipped with a laser rangefinder on a gyrostabilized platform, which serves to determine distances to the groundbased object of interest. The coordinates of a groundbased object are being determined by the combined application of anglerangefinder and integral rangefinder methods for coordinates determining. At the initial stages, the groundbased object coordinates are being estimated by the anglerangefinder method with some insufficient accuracy. Further, accumulations of measurements and refinement of the coordinates of the groundbased object are performed by the integral rangefinder method. The article presents the studies of the flight altitude, speed of an unmanned aerial vehicle and the accuracy of navigation equipment of consumers of global navigation satellite systems impact on the achieved accuracy of the obtained estimates of the coordinates of a groundbased reconnaissance object. Practical recommendations on the unmanned aerial vehicle piloting for achieving maximum accuracy of the coordinates of the groundbased object being explored are given based on the results of the studies. The issue on the necessary monitoring duration at various flight altitudes and the flyby radius to achieve the best accuracy of coordinates assessment was studied as well. 
Koshkarov A. S., Semenova V. P. Development of a simulation model of the lidar collision warning system of a service vehicle. Trudy MAI, 2023, no 128 The article describes the order of mathematical model developing of the lidar for the collision warning system of a service vehicle on the aerodrome territory while the aircraft maintenance. Based on the considered specifics of traffic organization of the service vehicles on the aerodrome territory and engineering software pack MATLAB, a model of a fuel tanker movement while the TU204 aircraft operation at the moment of peak service schedule congestion. The relevance of the presented model consists in the following. Transition to the new economic paradigm and digital economy is impossible without the expansion of air transportation. Increasing traffic flows require precise organization and constant control in the loading and maintenance areas. More and more machinery and engineering personnel are required. A logical solution to this problem is automation of processes, including autonomous driving functions delegating to service and transport vehicles. In modern aviation community, more and more attention is being paid to research and development of endtoend automation processes with minimum human intervention — hyperautomation. Thus, this trend is one of the priorities of the strategy of scientific and technological development in the Russian Federation. The problems solving complexity in this area is being characterized by limited visual observation, which consists in the lack of opportunity for the crew to see the maneuvering equipment on the route of movement, and the lack of forbidden zones. Thus, this article considers the possibility of improving the traffic of service vehicles control system and aircraft on the territory of the aerodrome by placing collision avoidance equipment at the movement of service and maintenance vehicles, based on the lidar application and capabilities assessing of the method of employing sensors of incoming information on the parameters of the external environment. 
Vataeva E. Y. Development of a mathematical model of the lidar of the collision avoidance system of the vehicle. Trudy MAI, 2023, no 128 Active technological development and improvement of technologies in various industries implies the use of nonlinear discrete, discretecontinuous and impulse automatic control systems (ACS), the dynamics of which is described by highorder differential equations. In the modern theory of automatic control, the problem of synthesizing the parameters of the control laws of impulse systems containing elements and devices with nonlinear static and dynamic characteristics is a complex scientific and engineering problem. In this regard, in order to successfully solve this problem for the entire range of quality indicators and for the whole variety of systems from a unified mathematical and methodological position, it is necessary to develop new methods.The development of Automatic control systems (ACS) control laws is directly related to the method of approximating a nonlinear characteristic, since it is necessary to maintain the degree of adequacy of the mathematical model. Since there are no universal approaches to the issue of approximation, for each specific case, it is required to take into account the specific modes of operation of the system. As you know, the most widely used piecewise linear approximation, however, the accuracy of the result obtained with such a mathematical model is not always sufficient. The various methods of approximation are considered, including irrational, integral, and analytical ones. This article proposes to use a polynomial approximation. As a method for synthesizing nonlinear systems, it is proposed to use the generalized Galerkin method, which makes it possible to synthesize control laws for automatic control systems of different classes (continuous automatic control systems and systems with various types of signal modulation, the dynamics of which is described by both linear and nonlinear equations of an arbitrarily high order). 
Issa H. A., AbdAli L. M., Yakimovich B. A., Kuvshinov V. V., Morozova N. V., Fedotikova M. V. Comparison of the effectiveness of various methods for controlling the energy parameters of photovoltaic systems. Trudy MAI, 2023, no 128 The silicon photovoltaic converters application for power supply systems requires a significant energyconversion efficiency. However, solar batteries without effective control systems and automatics do not comply with the technological requirements place on them. All that significantly reduces the efficiency of the electrical energy final generation and is not able ensuring power supply to auxiliary equipment of such complex systems as space and aviation equipment, communication power systems and other hightech complexes. The requirements for the energy supply of hightech facilities with solar power supply systems may be increased by employing new methods for control systems of solar power generation complexes. The peak power point tracking (MPT) method is often used to increase the amount of electrical energy that can be obtained from photovoltaic panels under certain conditions, as well as to improve the performance of solar panels. The photovoltaic system efficiency lies in the maximum power transfer to the load, hence is the interest in implementing more efficient TMM methods in terms of accuracy and speed. In this context, two TMM methods are applied to the photovoltaic DC converter, namely Fuzzy Logic Control (FLC) and Perturbation and Observation (P&O). A model for the boost converter is developed in MATLAB/Simulink to test and analyze the performance of the controllers. In the presented work, two controllers were tested under different irradiation conditions from the viewpoint of response time and efficiency. The results of this work prove that both control methods allow perfect tracking of the TMM with a slight FLC advantage over classical P&O. The proposed methods for the solar generation systems control allow significant operation efficiency rising of the whole system and increasing the final electric power component. This component is necessary for the qualitative provision of hightech objects and complex electric power systems, particularly, such as aviation and space engineering, satellite and spacecraft communication systems, as well as energyconversion efficiency increasing at the other objects, located on the ground and employing photoelectric generation systems. 
Vatutin M. A., Klyuchnikov A. I., Petrov D. G., Sudar Y. M. Circuit design methodology for an integrating pendulum accelerometer. Trudy MAI, 2023, no 128 The task of navigation consists in determining the true parameters of the of the aircraft center of mass motion and allows determining such navigation parameters as the linear coordinates of the place, as well as the magnitude and direction of the flight velocity vector in the selected coordinate system. The acceleration value being obtained from the accelerometer must be integrated twice to determine the linear coordinate. The pendulum positional accelerometer is convenient to be employed for the integrating mode of its operation. It is convenient to employ in the available accelerometer the measured acceleration integrating mode rather than the measuring mode itself for obtaining the first integral of the apparent acceleration being measured. For this purpose, an integrating capacitor with signal conversion circuits and periodic reset of the accumulated voltage is usually included in the feedback circuit. The article considers schematic solutions in the electrical circuit of the signal conversion device of a positional pendulum accelerometer for obtaining an integrating mode of its operation. The converting device circuit is based on the selfoscillating ramp generator with controlled input, which consist of two basic parts, namely integrator and Shmitt trigger. The output signal of the ramp generator is a time interval. Accelerometer connection to the ramp generator allows forming on its output a signal in the form of relative time interval change proportional to the apparent acceleration integral, i.e. the apparent velocity. Characteristics analysis of the accelerometers applied in the stateoftheart technology reveals that at maximum input exposure, the current value of the torque sensor takes values in the tens of milliamps, depending on the specific type of accelerometer and the measurement range. For the electronic circuit of the integrating accelerometer with ramp generator, this means that the operational amplifiers of the ramp generator, actually consume currents of tens of milliamps throughout the time to ensure the circuit operation. The article considered schematic solutions for ramp generator connecting the accelerometer, which significantly reduce the current consumed by the ramp generator while operation, namely buffer amplifier; electronic current divider, and connection via a current sensor. A technique for schematic design of the integrating pendulum accelerometer has been developed. 
Nestruev D. S., Borzov D. B. Model of reorganization of elements of a wireless computing cluster with an orbital arrangement of elements. Trudy MAI, 2023, no 128 A cluster is a modular multiprocessor system created on the ground of standard computing nodes connected by a highspeed communication medium. A typical cluster is a set of computers or processor cores under centralized control, which the user perceives as a single entity. The main characteristic of a computing cluster is fault tolerance. To ensure greater survivability, cluster elements must be able to move in space and be reserved. This concerns, first of all, the control element (Host) and the nodes in which the accumulated information is stored (Storage). Scientific novelty consists in the method of orbital dynamic reconfiguration of roles. This method allows distributing the cluster elements in orbits relative to the control element, which, in turn, ensures a better connection with the rest of the cluster elements. Comparison is performed by the simulation results. Modeling is carried out with the developed computer program. Parameter of the wireless computing cluster running time in an extraordinary situation (disappearance of a signal between cluster elements, change in the cluster element position, etc.) is used as the comparison parameter. The article considers an algorithmic model for initializing a wireless computing cluster with dynamic reconfiguration of roles by the orbital method, which significantly increases the fault tolerance of the cluster. The authors performed the analysis and comparison of the results of the described algorithm operation with existing ones. The results of the analysis revealed that dynamic reconfiguration of roles allows increasing the fault tolerance of a wireless computing cluster due to the fact that any of the elements are able to act as the ICD control element. 
Bukirev A. S., Savchenko A. Y., Yatsechko M. I. Application of the intelligent diagnostic system of informationconverting aviation systems of integrated avionics under external disturbing influences. Trudy MAI, 2023, no 128 The problem of low depth of search for the place of failure by modern onboard automated control systems of aviation equipment, which negatively affects the intensity of recovery and combat readiness, is considered. The emerging need for operational diagnostics of the technical condition of informationconverting aviation systems is a consequence of the increasing binding of a large number of systems to digital support and control, and the relegation of analog systems of modern avionics to the background. The need to diagnose the technical condition in real time, as well as the possibility of diagnosing systems on the ground, as well as during flights to perform special tasks, is an urgent problem, existing and proven practice, as well as data from enterprises that operate aviation equipment .The paper studies a model of an intelligent diagnostic system of informationconverting aviation systems of integrated avionics, operating under external disturbances, with an assessment of the quality of adaptation of an artificial neural network to limiting external disturbances, in order to solve the problem of improving the efficiency of technical diagnostics by the criterion of minimizing the time of diagnosis and increasing the probability of timely departure of an aircraft to perform special tasks. The stability of the functioning of the model of an intelligent diagnostic system to external disturbing influences is substantiated by simulating the above process in the Simulink package of the MATLAB programming environment. The paper outlines the basic principles of the approach to building an intelligent diagnostic system for informationconverting aviation systems of integrated modular avionics onboard equipment using artificial neural networks. Solving the problem of creating a model of an intelligent diagnostic system will make it possible to achieve the goal of moving to the creation of new diagnostic principles incorporated into modern onboard automated control tools. 
Kabanov A. A., Amosov M. V. VR/AR in the study, creation and operation of aerospace technology: from macrolevel to microlevel, from observation to activity. Trudy MAI, 2023, no 128 The study is aimed at the efficiency improving of the processes of creating aerospace technology and educational activities with digital VR/AR technologies in the aerospace industry. For this purpose, a review of applied examples of the VR/AR employing was performed according to the scheme: process, object, stage of the object’s life cycle, scale of the environment and object, goals, tasks, methods, technologies, software and hardware, and their critical analysis. Analysis of the results revealed that the predominant area of the VR/AR application in the aerospace industry was the groundbased workout of the assembling and mounting process of the bulky objects, as well as their operation under space conditions on the macrolevel. The article demonstrates herewith that in virtual or augmented space the operator performs directly the role of the object human operator. It shows as well that processes workingout and studying at the macrolevel, such as while the structuraltechnological design of products, acquire less spread, and they are the area where VR/AR are not employed to the full extent and possess substantial potential. The authors demonstrate that in this case operator in both virtual and augmented space should be an active observer and/or be a part of the structure or operation media. To realize this, the authors propose employing methods and techniques of the theory of inventive problem solving as the methodological foundation, and existing numerical modeling tools for physicochemical processes with their appropriate adaptation as the instrumental support. With regard to the educational activities, it was revealed that the main obstacle to the VR/AR implementation was the necessity for the costly infrastructure, namely laboratories and equipment. The authors suggested methodological recommendations and their software and hardware support, offering an opportunity for the AR/VR realization in the independent selfsufficient research work of the student employing the means of individual use. 
Kopeika E. A., Verbin A. V. Methodological approach to estimating the probability of failurefree operation of complex technical systems taking into account the characteristics of the control system based on the bayesian belief network. Trudy MAI, 2023, no 128 In developing complex technical systems together with their life cycle followup, the required reliability level provision is necessary. This requires developing new approaches associating reliability indicators of complex technical systems (CTS) with the checking system indicators. The article considers the possibility of accounting for the uncertainty of knowledge of the probabilistic data parameters, employed for the decisions substantiation. The proposed approach and models are based on the basic concepts and ratios of the theory of reliability and technical systems control. The methodological approach is based on the wellknown and tested apparatus of the Bayesian approach A methodical approach, which associates the probability of reliable operation of the complex technical system elements and reliability of complex technical system checking was developed. Analysis of the results allows making conclusion on the degree of the checking process characteristics effect on probability of faultfree operation of the complex technical system. The proposed d methodological approach may be employed at the CTS design stage, and it provides an opportunity for operating organization information obtaining on the CTS faultfree operation probability when receiving information on the CTS blocks is received, which allows making operative decision on the CTS condition. The obtained result may be of practical interested for military representatives, state certification authorities, industry representatives and may be employed while formation and justification of reliability requirements in tactical and technical tasks to develop (update) complex technical system. It may be employed as well for accounting for control process characteristics impact on the probability of the faultfree operation of the complex technical system at all stages of its life cycle. 
Knyazev A. S. Features of the use of simulators of multifunctional indicators in the process of personnel training. Trudy MAI, 2023, no 128 Cabins of modern types of weapons and military engineering are equipped with multifunctional indicators (MFI). Training personnel to work with the MFI is necessary; however employing costly complex simulators for this purpose leads ineffective exhaustion of their resources. Working with the MFI allows laying the route of movement, entering coordinates of targets, landmarks and radiobeacons, The MFI employing allows the crew to solve the tasks of navigation and combat employment. With this regard, more attention should be paid to learning how to work with the MFI while mastering modern types of aircraft. The best way of learning is application of real equipment or a complex simulator of the air force cabin, however, this may lead to inefficient exhaustion of their resource. There is a generally accepted practice of employing units, devices and systems dismantled from decommissioned samples of military equipment in training sessions. However, the MFI removed from the military equipment cannot be employed without special equipment (power supplies, computers, sources and signal converters). Thus, it is advisable to use MFI simulators, in which the functions necessary for the training goals achieving, for the studies instead of real MFI. They may be employed at both theoretical stage of the studies and practical training. Besides, the MFI simulators may be employed in the beginning of the simulator training to workout checkups and data entering, to relieve partially the costly complex simulator from these tasks. The article considers the issue of the MFI simulator application expediency while cadetpilots training for the DA42T aircraft. The IBM 4820 monitor, the closest in size to the real MFI of the DA42T aircraft, is selected as the basis of the developed MFI simulator. The SimInTech program, designed for technical systems modeling, was chosen as the software for the of information frames reproduction and development on the MFI. The fullscale mockup of the DA42T aircraft cabin was developed with the developed MFI simulators. Application of the MFI simulator and cabin layouts on their basis in training sessions ensures the achievement of various training tasks, which can be effectively employed in the training of personnel. The MFI simulator and cabin layouts employing saves on the one hand the resource of the expensive equipment, and on the other hand, represents the only opportunity for visual training due to the lack of complex simulators or real samples of military equipment in the training base. The obtained results of the work may be employed further for the development of the MFI imitators for various types of military equipment. 
Ledkov A. S., Belov A. A., Tchannikov I. A. Comparison of laser ablation and ion beam efficiency for contactless space debris deorbiting from a quasicircular orbit. Trudy MAI, 2022, no 127 The article deals with the problem of space debris removal from the nearEarth orbits. The motion of mechanical system, consisting of a spacecraft and an object of space debris sphere, is under study. Active spacecraft is a material point, while space debris is of a spherical shape moves moves on a circular orbit. In the first case, the contactless transportation of space debris is being realized by the laser, and in the second case, an electrojet engine jet is used. It is assumed that in the process of the ion transportation, the entire ion beam hits the surface of the sphere, and a simplified autosimilar model of plasma propagation is used to describe the far region of the electrojet engine plume. In the case transportation by laser, the laser beam control system ensures a point selection on the sphere, for which the normal is directed along the local horizon. The purpose of the study consists in comparing these transportation methods effectiveness in terms of the fuel rate of the active spacecraft. For this purpose, mathematical model of the mechanical system is being developed, and numerical simulation of the descent is performed. The numerical modeling results revealed that the laser ablation method appeared more effective compared to the ion transportation. It is associated with the fact that the force generated by the laser ablation effect appears greater than that generated by the ion beam. Besides, the engine generating the ion beam creates thrust, which should be compensated by the oppositely directed engine. It is supposed in the development of this work to account for the effect of aerodynamic drag forces acting of the active spacecraft and a space debris object, as well as studying special motion of the system and developing control law for the active spacecraft to sustain the required position out of the orbit plane. 
Averyanov I. O. Cargo with dampers parachute vertical landing dynamics research. Trudy MAI, 2022, no 127 There are a lot of researches related to parachute landing dynamics and almost all of them consider the system of parachutecargo (SPC) that works on its flight regimes, before it contacts the landing area. There are a few researches that consider the task of SPC landing, where a pneumatic actuator is used instead of the cargo. Nevertheless these researches are focused on the behavior of canopy. In case of cargo with dampers landing researches dropped cargo regime is considered. This is a commonly used practice to consider this regime on design phase of a cargo damper system. This article considers a parachute landing process for the cargo with dampers on the phase of its contact with the landing area. The aim of this research is to compare these two regimes of landing — with and without parachute influence to the landing process — to define the load cases for damper system (air fiber dampers are considered). This work considers only a vertical parachute landing process. Mathematical model (MM) of the parachute landing process consists of differential equations of motion for two separate objects — the cargo and the canopy. The canopy is symmetrical. Air dampers are attached to the cargo. Both objects are considered as absolutely rigid. Straps are modeled as a function of distance between the corresponding points on the cargo and on the canopy. Parachute straps are elastic. Euler’s ratios are used to transform the angular velocities to the angles. Here the two tasks are considered: 1 — the drop case is presented to show that MM gives reliable results for the considered structure of the cargo and the system of air dampers; 2 — parachute landing. Comparison of the calculation results and experimental data shows their good correlation. Analysis shows that the parachute system has an essential influence on landing process dynamics of the cargo with dampers. This influence has to be taken into account in the case of damper’s design phase, analysis of cargo drop tests. It recommends to use this MM for statistical mathematical modelling of the parachute landing process in the task of reliability index evaluating. 
Popov I. P. A fragment of the dynamics of an aerodrome tractor with massive towed objects. Trudy MAI, 2022, no 127 It is noted that the most difficult stage in the operation of an airfield tractor with massive towed objects is the starting mode. This is due to the need to overcome the static friction force, which significantly exceeds the motion friction force. As a solution to this problem, we can consider the use of the initial kinetic energy of the tractor, which can develop when using limited elastically deformable traction coupling devices. To optimize the mathematical model, the following assumptions are made: traction force F on the hook of the tractor is a constant value; the inertial masses of the tractor and towed objects are the same and equal m. To evaluate the effectiveness of the use of elastically deformable traction coupling devices, the obtained results are compared with similar results corresponding to an absolutely rigid traction coupling device. The use of elastically deformable traction coupling devices makes it possible to accumulate the initial kinetic energy of an airfield tractor, which makes it possible to overcome the static friction force and ensure the starting of heavy towed objects. Comparison of the kinematic and dynamic parameters of the tractor with towed objects for options with absolutely rigid and resiliently deformable traction coupling devices shows that the efficiency of using the latter increases with an increase in the number of towed objects. Elastically deformable towing devices can cause oscillations of the tractortowed objects system. To prevent them, the towing devices must be hard blocked at the moment they reach the greatest deformation. 
Bogachev V. A., Petrov Y. A., Bernikov A. S., Sergeev D. V. Investigation of the influence of various factors on the descent of the planetoid along the ladders of the lander. Trudy MAI, 2022, no 127 To ensure a reliable exit of the vehicle along the ladders to the surface of the planets and their satellites, it is necessary to account for the effect of a large number of various factors, such as:
The undercarriage of the planetoid, as a rule, consists of six or eight driving wheels and an elastic suspension. An electromechanical drive is installed in the hub of each wheel, ensuring thereby high crosscountry ability and high reliability. One of the main problems consists in the reliable exit ensuring along the ladders to the surface of the planet (satellite). For this purpose, experimental selection of materials being installed on ladders that ensure a reliable grip without slipping with the wheels of the planetoid is necessary. To confirm the lunar rover guaranteed exit, The model allowed reproducing angular position of the landing unit supports, ladders and slope. A decision was taken on what shock absorbers should be «shotoff» to reduce clearance and thereby align the position of the vehicle on the landing surface. After that, the ladders, along which the lunar rover successfully moved to the Moon surface the were opened. Thus, when designing a landing unit for a spacecraft with a planet rover, it is necessary to envisage pyrotechnics in the design of shock absorbers that can be employed to improve the planet rover exiting conditions along the ramps. Shock absorbers with pyro nodes may also be employed in case of the groundintake device and other mechanisms presence onboard the vehicle. Tests on the material selection and the determination of the coefficient of adhesion were conducted with the technological wheel of the planetoid and fragments of ladders, on the working surface of which different materials were placed. With this purpose, testing programs and methods were developed, and a test bench, which ensured computed loadings and temperatures, was fabricated. To analyze the planetoid descent along the ladders on the loose soil, the ladder was tested at its interaction with loose soil. During the tests, the ladder and rested on the soilanalogue placed in a container. The top layer of the soil represented a loose finely dispersed soil, which is being characterized by low adhesion and rather high internal friction with low loadbearing capacity and high compressibility. If the vehicle lands on rock outcrops or there is a hard surface, such as a stone, under the end of the ladder, then the ladder lateral movement will be much greater than this in the case of a loose soil. With the landing stage roll and heavy loads on one side, the movement of the ladder ends may be significant and the vehicle might leave the track, which will lead to an accident. As the result of the analysis of the planet rover exit along the ladders, the gaps between the wheel of the planetoid chassis and the structural elements of the landing unit were determined for the case of the landing platform roll in a plane perpendicular to the installation of the ladders at an angle of 20°. The tolerances for the installation of ladders on the platform, backlash in the nodes of rotation of the ladder links, as well as the rigidity characteristics of the ladder (power beam and railing) were accounted for herewith. The article presents the results of the fullscale experimental studies of the various factors impact on the of a planet rover exit on the surface of planets and their satellites. As the result of the tests, the coupling coefficients were determined at different temperatures and loads between the fragments of the ladder layout made of various materials and the wheel. The article considers typical characteristics of the touchdown surface, such as slope, the soil bearing capacity and the presence of stones, and proposes the ladder working surface materials ensuring calculated coefficients of adhesion to the planet rover wheel. The technique for conducting tests on determining the coefficient of adhesion of the planet rover wheel is presented. Recommendations with regard to the structural design of the landing gear shock absorbers and the ladders fixing in the working position have been elaborated. 
Kriven G. I. Evaluation of damping properties of composites. Trudy MAI, 2022, no 127 The article studies fibrous composites, particularly, analyzes their effective damping properties, natural frequencies and loss coefficients. Both effective dissipative and wave properties are being defined by the presence of a viscoelastic layer laid between the elastic fiber of high rigidity and a less rigid matrix. Analytical evaluations employing linear visoelastic analogy method are being presented. The author revealed that the three phases method was more preferable than the Race method for determining parameters with high accuracy. Whiskerized systems, grown on the fiber surface and submerged into the viscoelastic layer, were proposed for use to enhance dissipative properties and retain mechanical ones. The author conducted studies on oscillations damping of the stratified composite hinged beam. The viscoelastic interlayer is being inserted into the composite beam to enhance its damping properties. Resonant frequency and modal losses coefficient of the beam are being evaluated by the BernoulliEuler beam model and Timoshenko model. It is noted that in case of transversely oriented fibers both models, i.e. the BernoulliEuler beam model and Timoshenko model, account for the shear deformations. 
Kolodezhnov V. N., Veretennikov A. S. The translational motion of a cylinder along its axis in a space filled with a nonlinear viscoplastic fluid. Trudy MAI, 2022, no 127 The article studies fibrous composites, particularly, analyzes their effective damping properties, natural frequencies and loss coefficients. Both effective dissipative and wave properties are being defined by the presence of a viscoelastic layer laid between the elastic fiber of high rigidity and a less rigid matrix. Analytical evaluations employing linear visoelastic analogy method are being presented. The author revealed that the three phases method was more preferable than the Race method for determining parameters with high accuracy. Whiskerized systems, grown on the fiber surface and submerged into the viscoelastic layer, were proposed for use to enhance dissipative properties and retain mechanical ones. The author conducted studies on oscillations damping of the stratified composite hinged beam. The viscoelastic interlayer is being inserted into the composite beam to enhance its damping properties. Resonant frequency and modal losses coefficient of the beam are being evaluated by the BernoulliEuler beam model and Timoshenko model. It is noted that in case of transversely oriented fibers both models, i.e. the BernoulliEuler beam model and Timoshenko model, account for the shear deformations. 
Alexandrov L. G., Konstantinov S. B., Markov A. V., Platov I. V. About the method of confirming the operability of the phase separator of an intank capillary device. Trudy MAI, 2022, no 127 For propulsion systems of space craft multiple burns engine, the condition for normal operation is the supply of liquid propellant components to the consumable lines without disturbing the continuity of the flow. The article discusses the method of conducting control tests of the phase separator of the capillarytype intank device at the stage of full readiness of the fuel tank. One of the most important stages in the creation of fuel tanks is their ground experimental testing, carried out under conditions close to operating conditions. The main purpose of such tests is to confirm the compliance of the technical characteristics of the tank with the required values specified in the technical specification for its development. As a criterion for assessing the quality of the phase separator, the efficiency coefficient was chosen, which is the ratio of the capillary holding capacity of the mesh field of the phase separator material to the hydraulic resistance of the phase separator to the flow of liquid passing through it and containing gas inclusions. The methodology given in the article for determining the operability of a capillary phase separation device at the stage of control tests of a finished fuel tank makes it possible to guarantee the required performance indicators of an intank capillary device at the stage of factory ground tests, which improves the quality of finished products. The result of this work is a decision on the compliance of the tested prototype tank with the specified requirements and the possibility of its fullscale operation as part of the propulsion system of the spacecraft. 
Rotermel A. R., Sevchenko V. I., Lizan V. M. Modernization of the working part of the wind tunnel for tensometric measurements of aerodynamic forces in supersonic flow. Trudy MAI, 2022, no 127 The article considers the result of the modernization of strain gauges installed in the working part of the supersonic wind tunnel (AT) ST3, which allows to increase the range of experimental studies on the angle of attack of the model under study from 0 to 20 degrees. Numerical studies of the flow of the model in the working part of the pipe have been carried out in order to verify that the model is located inside the rhombus of an undisturbed flow. The supersonic AT ST3 is widely used to create gas flows of specified parameters for the experimental study of the flow around models of aircraft elements in the range of Mach numbers from 1.5 to 4.2. To increase the range of experimental possibilities, the authors proposed to increase the range of angles of attack of the model under study, taking into account its finding inside the rhombus of a uniform part of the flow. The supersonic AT ST3 makes it possible to determine the aerodynamic forces acting on the model under study at angles of attack in the range from — 10° to +10°, which limits the field of study. The range of angles of attack is determined by the boundary of the rhombus of the uniform part of the flow in the working part of the pipe. To ensure the adequacy of the simulation, the conditions of adhesion and isothermicity were used on the surface of the body and the walls of the working part of the pipe. According to the values of pressure (p_{0}=14 kgf /cm^{2}) and temperature (T_{0}=283K) of the gas in the receiver, the flow parameters in the working part of the pipe were calculated (M_{∞}=4.2; p_{∞}=6467 Pa; T_{∞}=61.8 K; a_{∞}=8 m/s), and also determined the arrangement of the rhombus of the uniform part of the flow. For the calculations, the NavierStokes equations were used, which are closed by the turbulence equations kω SST. The calculation scheme is shown in Figure 5. A sphere with a radius of R = 20 mm was chosen as the model. Modeling was carried out using a structured prismatic finite element grid of 1032 thousand elements (26 elements accounted for the thickness of the boundary layer (parameter y+=0.3)). Modernization of the fastening system of strain gauges located in the path of the supersonic AT ST3, taking into account the requirements of permissible «cluttering» of the working part of the pipe, will allow experimental studies to determine the aerodynamic forces acting on the model at angles of attack up to 20°, which is of interest when conducting studies of the aerodynamic spectrum. 
Khafaga A. S., Ilyin A. G. Improving and processing of weak digital pulse signals using a narrowband noise structure. Trudy MAI, 2022, no 127 The article considers the result of the modernization of strain gauges installed in the working part of the supersonic wind tunnel (AT) ST3, which allows to increase the range of experimental studies on the angle of attack of the model under study from 0 to 20 degrees. Numerical studies of the flow of the model in the working part of the pipe have been carried out in order to verify that the model is located inside the rhombus of an undisturbed flow. The supersonic AT ST3 is widely used to create gas flows of specified parameters for the experimental study of the flow around models of aircraft elements in the range of Mach numbers from 1.5 to 4.2. To increase the range of experimental possibilities, the authors proposed to increase the range of angles of attack of the model under study, taking into account its finding inside the rhombus of a uniform part of the flow. The supersonic AT ST3 makes it possible to determine the aerodynamic forces acting on the model under study at angles of attack in the range from — 10° to +10°, which limits the field of study. The range of angles of attack is determined by the boundary of the rhombus of the uniform part of the flow in the working part of the pipe. To ensure the adequacy of the simulation, the conditions of adhesion and isothermicity were used on the surface of the body and the walls of the working part of the pipe. According to the values of pressure (p_{0}=14 kgf /cm^{2}) and temperature (T_{0}=283K) of the gas in the receiver, the flow parameters in the working part of the pipe were calculated (M_{∞}=4.2; p_{∞}=6467 Pa; T_{∞}=61.8 K; a_{∞}=8 m/s), and also determined the arrangement of the rhombus of the uniform part of the flow. For the calculations, the NavierStokes equations were used, which are closed by the turbulence equations kω SST. The calculation scheme is shown in Figure 5. A sphere with a radius of R = 20 mm was chosen as the model. Modeling was carried out using a structured prismatic finite element grid of 1032 thousand elements (26 elements accounted for the thickness of the boundary layer (parameter y+=0.3)). Modernization of the fastening system of strain gauges located in the path of the supersonic AT ST3, taking into account the requirements of permissible «cluttering» of the working part of the pipe, will allow experimental studies to determine the aerodynamic forces acting on the model at angles of attack up to 20°, which is of interest when conducting studies of the aerodynamic spectrum. 
Brodsky M. S., Zvonarev V. V., Khubbiev R. V., Sherstuk A. V. Computer model of the satellite communication and data relay system radio channel during multiposition signal transmission. Trudy MAI, 2022, no 127 The paper proposes mathematical model of radio channel of the communication and data relay satellite system (CDRSS) in case of multiposition signal transmission by several spatially separated radioelectronic equipments. Based on the proposed mathematical model, computer model has been developed for estimating the noise immunity of signal reception under given technical limitations. The computer model under consideration makes it possible to calculate with high accuracy the values of the energy characteristics of radioelectronic equipments, such as the average radiated power of the equipments; transmitting (receiving) antenna gain; effective isotropically radiated power; ratio of signal bit energy to noise power spectral density; the ratio of the total signal power to the noise power at the input of the receiving device, at which the required noise immunity of the CDRSS facilities is ensured. A quantitative measure of radioelectronic equipments noise immunity is the probability of a bit error. To calculate the probability of a bit error, an algorithm for estimating the noise immunity of signal reception has been developed, which, unlike the existing ones, allows calculating the probability of a bit error for radioelectronic equipments spaceseparated emitting pairwise correlated signals in the direction of the receiving antenna of the satellite CDRSS. The proposed algorithm allows you to calculate:
The article gives an example of calculating bit error probability during multiposition signal transmission in the direction of the receiving antenna of satellite CDRSS, oriented towards the orbital electronic equipments. The simulation results testify to the correctness of the approach and make it possible to carry out systematic studies of the dependence of the energy characteristics of the receiving equipments of the CDRSS on the number of lowpower transmitting equipments emitting pairwise correlated signals. The proposed computer model can be used:

Dmitriev A. O. Proposal to provide power supply to a network of clusters of small spacecraft with a tandem spacecraft. Trudy MAI, 2022, no 127 This article proposes the construction of a tandem of spacecraft consisting of an autonomous satellite with a large area of solar phototransformers and an autonomous satellite for transmitting the received energy to small spacecraft using laser radiation. This tandem is connected by a contactless magnetic resonance method of energy transfer. To provide the cluster with energy, it is planned to develop a modular, i.e. not mechanically integrated into a single whole, satellite complex — a tandem with a contactless power transmission line. The tandem should consist of spacecraft moving in close orbits interacting with each other via wireless communication and energy transmission lines. The main task of this tandem is to supply energy to a cluster of small spacecraft performing target tasks. Then conceptually such a complex will have the following structure:
Although at first glance the integral execution of the photodetectoremitter system suggests itself, in practice this is a nontrivial task. Such a largesized design, which will experience serious temperature changes and at the same time have high requirements for targeting the receivers of the cluster spacecraft, will require a complex stabilization and guidance system. The advantage of fragmentary tandem construction is the absence of such serious requirements and the ability to increase the coverage angle with laser or microwave radiation for cluster satellites. It is also possible to use several satellite emitters for greater coverage of consumers from a cluster of small spacecraft. 
Abramov A. A., Yakush N. A. Development of USRP verification methodology for highprecision radio system research. Trudy MAI, 2022, no 127 Currently, in telecommunications, there are problems of inefficient use of spectrum [3], the inability to flexibly control hardware devices, which have led to an increasing interest in softwarecontrolled radio (SDR), which has proven itself as a reliable system for thorough analysis of radio frequency signals with the possibility of flexible control and modification [4]. One of the prominent representatives of SDR is the highprecision and inexpensive USRP 2901 model from the 29xx series from National Instruments, capable of solving the problems of prototyping radio systems, radio reconnaissance, direction finding, creating local positioning systems, developing coherent multichannel transceiver systems and solving other important problems in the aerospace sphere. This work is devoted to the development and testing of the method of verification of USRP 29xx series devices for highprecision experimental studies for solving problems of a wide range in the field of information communications using the Omega radio complex. The subject of the study is the evaluation of the effectiveness of using SDR on the NI platform. To obtain the data closest to the true ones, to exclude the maximum number of different types of errors, the work analyzed in detail the plan and stages of experiments, in particular, the planning of experiments at the tactical level, the description of which is indicated in the publications [18, 19]. The calculation of the required sample ensures the required probability and reliability of the results [20]. However, there is no information in the technical documentation for USRP devices that they can be used for highprecision research. After planning the experiments, a method for verifying devices was developed, which included specific 6 stages of experiments that evaluate physical values that characterize the accuracy and quality of USRP equipment. The following results were obtained as a result of testing this method:

Vakulchik O. V. Cybersecurity of the functioning of the information management system with the SQL Server. Trudy MAI, 2022, no 127 This article regards the issue of cybersecurity of the information management system of the aerospace system (IMS). Database is the basic IMS component. The SQL server was employed as the database system. Monitoring execution is necessary for the Database information processes performance and security support. The article describes the development of the remote monitoring effective method. This method solves two basic problems, namely information transmission security in the open environment, and effective assessment of the information environment state. Analysis revealed that effective remote monitoring ensuring requires tool selection. The selected tool should wield enhanced security and employ SQL language for the Database performance evaluation. The tool tackled with in this article ensures information encoding in the open transmission environment. It acts as an administrative panel as well. After the tool selection, the SQL language objects analysis was performed. Selection criteria of the necessary objects are as follows: the provided information completeness, request preparation complexity, and the internal functionality enhancing capability. Analysis revealed that storable system procedures are the most informative. The next stage of development consisted in the stored procedures selection according to the «integral informativity» criterion. The sp_whoisactive stored procedure is of specially great capabilities. However, it has been found that these procedures were redundant. That is why optimized requests for the remote monitoring effectiveness improving were developed. The optimized requests reduce the status information volume, ensuring security, and provide herewith the remote monitoring completeness. 
Burenko E. A. Substantiation of the effectiveness of the use of signals with orthogonal frequency division multiplexing in aviation radio systems of information transmission. Trudy MAI, 2022, no 127 Aviation complexes of communication facilities are subject to stringent requirements in terms of weight and size indicators and energy consumption. Along with this, to ensure highspeed data transmission between a ground control station (GCS) and an unmanned aerial vehicle (UAV) over long distances (up to 300 km), it is required to provide high energy in the radio channel. This paper discusses the main negative factors of aviation radio channels that reduce the efficiency of the radio system of information transmission, which can be eliminated as a result of the use of signalcode structures based on the use of signals with orthogonal frequency division multiplexing (OFDM). Such negative factors include the presence of fading of the radio signal at the input of the receiver of the radio system and the possible impact on the operation of the radio system of interference. Discusses the main characteristics and advantages of signals with OFDM over classical singlefrequency signals (for example, with binary phase shift keying — BPSK) are considered, as well as basic engineering and technical calculations are presented confirming the validity of the use of these signalcode structures in aviation radio systems for information transmission, as one of solutions for combating fading caused by multipath signal propagation, and as a result, with intersymbol interference (ISI), which manifests itself in the superposition of rereflected signals on the direct (main) signal. Discusses the methods for ensuring the noise immunity and secrecy of a radio system with OFDM based on the use of broadband pseudonoise signals (PNS) together with OFDM signals are considered. For example, Msequences or Gold’s sequences, which are widely used in radio systems for various purposes, can be used as PNS. To combat narrowband interference, signal jamming protection can be used, which is reduced to a significant increase in the band occupied by the OFDM signal. Band increases as a result of superposition of the PNS signal with base B ≫ 1 on each subcarrier of the OFDM. The simplest method for reducing the interference power in the receiving part is the narrowband interference decorrelation method, which reduces the interference power to the base B times as a result of multiplying the interference signal with the reference PNS in the demodulator PNS. As a result of multiplication, the interference is converted into a signal with a uniform power spectral density in the interference band, similar to the effect of white noise. 
Kazantsev A. M., Knysh M. V., Makarov M. K. Selection of the rational composition of the radio information sensor group of a spatially distributed monitoring system. Trudy MAI, 2022, no 127 In many application domains, group control problems arise under counteracting conditions. Examples are interaction processes of systems with conflicting and sometimes antagonistic target functions, such as a spatially distributed monitoring system (SDMS) and mobile airborne objects (MAO) penetrating into the system’s area of responsibility. However, in practice the resource of the SDMS, which determines the space review capabilities, can be limited, including due to low efficiency of groundbased radio information sensors (RIS) in detecting moving air objects at low altitudes. The specified problem can be solved by inclusion into the SDMS of mobile airborne RIS and joint application of airborne and groundbased RIS under unified control. Thus one of the most important tasks is the fullest realization of information possibilities of all RIS for the purpose of the maximum coverage of their working zones of airspace. The solution of this problem is possible at the expense of estimation of composition and forecasting of ways of actions and tactics of application of MAO with the purpose of definition of rational structure of heterogeneous grouping of RIS of SDMS. In the article a new methodical approach to the choice of rational composition of heterogeneous grouping of RIS of SDMS is proposed. In a basis of the offered decision methods of the theory of dynamic graphs and methods of vector discrete optimization are put. Features of formation of variants of structure of grouping of RIS are considered. An algorithm is offered, allowing on the basis of the minimum set of attributes of the adversary to choose a rational composition of heterogeneous grouping of RIS in accordance with the hierarchy of links «attributes of the of the opposing side’s activity — stages of preparation for use of MAO — variants of use of MAO». 
Glushkov A. N., Moiseev S. N., Ispulov A. A., Filippov A. V., Nikolaev S. V. Method for assessing the accuracy of the alignment of onboard radar systems of aircraft. Trudy MAI, 2022, no 127 The presented article proposes a method for the errors operational evaluation in the alignment of radar and optoelectronic stations applied in navigation and weaponaiming aircraft complexes. Its actuality is associated with the fact that the alignment accuracy of the location systems determines potential effectiveness of the aviation complexes, since the alignment errors cause the need to increase the location systems fields of vision and, as the result, lead to the aircraft in the potential efficiency decrease. These errors minimization will allow narrowing their fields of vision, while preserving radars search capabilities, and enhancing detecting capability and spatial resolution of optoelectronic systems by the integral background illumination reduction. As the result, both detection range and the probability of objects recognizing will be enhanced. The currently developed methods for the alignment errors evaluating do not allow performing operational correction of the of directional patterns relative position of the onboard location systems of navigation and weaponaiming complexes in real operating conditions, which requires new evaluation methods development. Natural requirements for these methods are the possibility of obtaining evaluations in real time or close to it, as well as the possibility of employing these evaluations for correcting relative location of the radars fields of view. Evaluation methods developed as of today do not meet these requirements, which stresses the relevance of the problem being solved. The problem of errors evaluation in the alignment of the onboard location systems is set and solved as a filtration problem, since in general case the object of the study is nonstationary. The authors developed an algorithm for mathematical formalization of the alignment errors behavior during the flight of an aircraft, allowing performing correction of the directional diagrams position of location systems in real time based on the values of their evaluation. Model experiments were conducted to confirm correctness of the developed solutions. 
Aslanova A. B. Optimization of the uav multisegment hovering mode in a heterogeneous flight zone. Trudy MAI, 2022, no 127 The presented article proposes a method for the errors operational evaluation in the alignment of radar and optoelectronic stations applied in navigation and weaponaiming aircraft complexes. Its actuality is associated with the fact that the alignment accuracy of the location systems determines potential effectiveness of the aviation complexes, since the alignment errors cause the need to increase the location systems fields of vision and, as the result, lead to the aircraft in the potential efficiency decrease. These errors minimization will allow narrowing their fields of vision, while preserving radars search capabilities, and enhancing detecting capability and spatial resolution of optoelectronic systems by the integral background illumination reduction. As the result, both detection range and the probability of objects recognizing will be enhanced. The currently developed methods for the alignment errors evaluating do not allow performing operational correction of the of directional patterns relative position of the onboard location systems of navigation and weaponaiming complexes in real operating conditions, which requires new evaluation methods development. Natural requirements for these methods are the possibility of obtaining evaluations in real time or close to it, as well as the possibility of employing these evaluations for correcting relative location of the radars fields of view. Evaluation methods developed as of today do not meet these requirements, which stresses the relevance of the problem being solved. The problem of errors evaluation in the alignment of the onboard location systems is set and solved as a filtration problem, since in general case the object of the study is nonstationary. The authors developed an algorithm for mathematical formalization of the alignment errors behavior during the flight of an aircraft, allowing performing correction of the directional diagrams position of location systems in real time based on the values of their evaluation. Model experiments were conducted to confirm correctness of the developed solutions. 
Gorbunov S. A., Nenashev V. A., Mazhitov M. V., Khadur A. A. Algorithm for estimating the coordinates of the state of the helicopter in the onboard radar station. Trudy MAI, 2022, no 127 Functions and application areas extension of helicopters determines the demand and relevance of the new algorithms developing for the state coordinates estimating in the airbased pulseDoppler radar station, ensuring stable surveillance, which in its turn will positively reflect on the flight safety. Helicopter is a complex object under observation in terms of radar. Analysis of the existing algorithms for the state coordinates estimating revealed insufficient efficiency in a helicopter detecting and tracking at various kind of flying. Thus, there is an objective need to develop new estimation algorithms that account for the helicopter flight characteristics and ensure its stable observation. The authors propose employing mathematical apparatus on the optimal linear filtering theory as an approach to optimal algorithms obtaining for the helicopter state coordinates estimation. The purpose of the study consists in synthesizing an algorithm optimal by the root mean square error minimum for coordinates estimation of the helicopter absolute and relative motion in the onboard radar station at various kinds of its flight, including the hovering mode, based on the mathematical apparatus on the optimal linear filtering theory. As the result, the article presents the analysis of effectiveness of the said synthesized algorithm application. The specificity consists in two components application, namely estimation of Doppler frequency, stipulated by signal reflection from the fuselage, and Doppler frequency stipulated by the signal reflection from the rotating helicopter blades. The results of the study may be employed while the existing radar stations upgrading, or developing prospective ones based on the pulseDoppler principle of signals processing. 
Vernigora L. V., Kasmerchuk P. V., Sysoev V. K. Analysis of groundbased optical means of observing laser beacons on board nearEarth spacecraft. Trudy MAI, 2022, no 127 A critical issue in the spacecraft navigation consists in precise determination of the spacecraft position in space. The spacecraft navigation parameters measuring in the nearEarth space may be realized employing both onboard and groundbased measurement facilities, which include radiotechnical and optical systems. In the loworbit region with orbits altitude less than 5000 km radar measurement means are being employed as a rule. At the altitudes above 5000 km, a spacecraft is out of the radar stations visibility zone. In case absence of the onboard radiotechnical means as a part of the spacecraft, ensuring current navigation parameters measuring, photometrical surveillance becomes the only susceptible possibility for the spacecraft monitoring and its technical state evaluation. Optical measuring instruments are capable of ensuring higher accuracy than with the radio band application. However, optical means of observation have a number of disadvantages, which significantly limit their capabilities. Such disadvantages are as follows: their dependence on the time of day, illumination of the spacecraft, and weather conditions. Besides, a smallsized spacecraft has utterly low visible brightness, which aggravates their observation by optical means. These shortcomings can be partially overcome by installing optical laser beacons onboard the nearEarth spacecraft, which will allow ensuring operational monitoring of their condition (both orbital and rotation parameters, including the case of communication deficiency with them) by the groundbased optical means Groundbased optical observation stations of the Space Monitoring System perform monitoring of all objects located in the nearEarth space to maintain a catalog of orbital parameters for subsequent prediction of their position. Obtaining long photometric series for the tasks of the Space Monitoring System is possible, but only by suspending the main tasks execution. Besides its own standard optical groundbased observation facilities, the Space Monitoring System extensively employs of the observations results obtained at optical observation stations of scientific organizations, particularly, the Pulkovo Cooperation of Optical Observers (PulCON), the Russian Academy of Sciences (INASAN, SibIZMIR), the Roscosmos Research Institute and university observatories. All these optical observation stations are equipped with modern telescopes and photodetectors that will allow for confident registration of radiation from laser beacons installed onboard the nearEarth spacecraft, thereby increasing the reliability of the nearEarth spacecraft positioning regardless of their size and orbit type. 
Javadov N. H., Agayev F. G., Huseynov H. A., Zulfugarli P. R. Issues of assessing the feasibility of tasks assigned to unmanned aerial vehicles. Trudy MAI, 2022, no 127 The article deals with the feasibility assessing of the tasks assigned to unmanned aerial vehicles (UAV), and presents a method for the quality assessment of the military purpose UAV. As the result of the said assessment, the resulting inference with account for the unmanned engineering requirements and preferences is being formed. Criteria, which include indicators such as conformity, capability, operational security, sustainability and readiness for solving the tasks assigned to the UAV are known as well. In this regard, it is especially important to address the issues of the used sensors capabilities matching to solve the tasks assigned to the UAV. This task is usually being solved by modeling. Besides, the descriptive structure of a special metric is employed as well to develop a criterion for the UAV tasks feasibility assessing. For example, the issue of the of UAV tasks feasibility while searching for some objects depending on the terrain real landscape should be solved by creating a special methodology for the terrain visualization assessing depending on the state of the surface relief under study. Solving the issue of tasks feasibility is closely associated with the issue of a rational compromise achieving between the UAV total load, various sensors and the UAV mission feasibility. The article studied the issue on the tasks feasibility assigned to the UAV by solving the problem of developing the new criterion of executing functions of objects detection on the surface of the soughtfor site by the UAV. Based on the wellknown empirical criterion of the said task feasibility, a new indicator has been formed as a logarithm of the ratio of the task fulfillment and nonfulfillment probabilities. Based on the proposed indicator, the invariant linking this indicator with the number of work cycles, which ensure the corresponding probabilities of the task fulfillment, has been formed. 
Maletin A. N., Glushchenko A. A., Mishina O. A. Investigation of the capabilities of modern space facilities for monitoring objects in nearEarth space . Trudy MAI, 2022, no 127 The researches of near and far outer space is relevant in scientific and practical terms. For science, it is the study of the Solar system (including asteroids, comets, distant Galaxies). From a practical point of view, this is the control of space objects and the monitoring of the contamination of nearearth space with space debris. The world’s leading space powers continue to work on the creation of space facilities designed to solve the problems of testing technologies for remote inspection, autonomous rendezvous with specified objects, maintenance, repair, reconfiguration, modernization, refueling, changing orbit parameters, monitoring «space debris» and other necessary operations. This approach can be used to extend the service life of serviced spacecraft. Based on the tactical and technical characteristics known from open sources, the article presents the results of the analysis of the current state and prospects for the development of foreign automatic spacecraft of a new generation developed on the basis of unified space platforms. The introduction of advanced technologies has made it possible to significantly reduce the mass and size characteristics of spacecraft and the consumption of all types of resources, which has reduced the cost of developing, manufacturing and launching small spacecraft. New miniaturization technologies make it possible to create small spacecraft capable of performing tasks that 20 years ago were available only to largeclass spacecraft. The mass of such devices does not exceed 100150 kg, the overall characteristics may be less than 1 m^{3}. At the same time, the period of active existence can reach 57 years, the reserve of the characteristic speed is more than 400 m/s, the positioning accuracy is no more than 1050 m, and the orientation accuracy is 1015 angular s. The optical—electronic means of spacecraft have high resolution, allowing to observe geostationary spacecraft from low Earth orbit. Theoretical and experimental studies have been brought to the stage of creating real groupings of small spacecraft that demonstrate very high capabilities for solving problems of monitoring nearEarth space. First of all, this indicates a high level of theoretical and applied scientific research in this direction and the prospects for the miniaturization of space technology. In addition, this fact explains the priority of these studies, both for the state and for private companies developing modern space systems and complexes. 
Travin A. A., Kalashnikov E. A., Bakradze L. G. Improvement of diagnostics of machine mechanisms using nondestructive testing methods. Trudy MAI, 2022, no 127 The article tackles the problems of analyzing the industrial machine operation by more correct selection of place for the vibration acceleration control , as well as specially developed methods for spectra processing, The material being proposed describes the solved issue on the sensor positioning for correct vibration measurement and analysis, The article presents the spectrum, which analysis allowed detecting the signals with frequencies close to each other within the limits of the spectrum analyzer resolution capability. Besides spectrum identification of the direct Fourier transform of the separate links vibration, the common amplitude of its series of oscillations in time applying inverse Fourier transform was employed for each link analysis To improve diagnostics, the vibration curves during the process were compared with the course of alloy crystallization while industrial experiments on a machine. To obtain extra data and further improvement of the diagnostics method under consideration, the temperature indicators of the temperature fields were gathered employing the FLIR brand infrared imaging equipment. The obtained data may be significant while the machine significant components state assessing. It is assumed as well that the infrared imaging equipment allows more accurate determining of the sensors location places for vibrations measuring. The operation of individual machine units is described, as well as general dependence plotting of the total vibration amplitude, its isolation to a large extent and, thus, identification of the work of both mold and rollers, and comparison of the obtained results with the measured spectra. The article considers the possibilities of computer programs for obtaining general curves of the mold unbalance motion and after further Fourier transform obtaining an excitation spectrum and a response spectrum. The work describes theoretically the metal melt motion, allowing obtaining a parabolic type differential equation. The equation was solved for the case of a pulsed vibration impact on the melt. 
Lazeev A. S., Litovka Y. V. The algorithm of transformation of polygonal models to simplify the calculation of galvanic processes. Trudy MAI, 2022, no 127 Electrochemical coatings provide special properties of the surface of the parts. In the aircraft industry, electroplating coatings are widely used to protect against corrosion and increase the wear resistance of steel and aluminum parts. Efficient specification of the shape of a part in automated control systems for galvanic processes can be organized by exporting drawings for subsequent software processing where complex mathematical calculations associated with surfaces are not required. To solve problems that require complex calculations, various polygonal meshes are divided into simpler shapes. An algorithm for calculating the electric field in a galvanic electrolyte is presented, and the need for a mathematical description of the cathode surface to set the boundary conditions is shown. The paper considers the issues of creating algorithms for converting threedimensional polygonal models into voxel format to reduce computational complexity, which is estimated by indicators: the time of the algorithm and the amount of memory occupied. The algorithm for converting a polygonal model into a voxel model has the form:
When comparing the most productive «naive» algorithm, which has complexity O(n(1/h)^{3}) with the algorithm developed in this article, which has complexity O((log n)∙(1/h)^{3}), an increase in efficiency up to four hundred thousand times. The resulting geometric mathematical model reduces the search time for optimal parameters of the galvanic cell, especially when using modern effective optimization methods. 
Molotkov A. A., Tretiyakova O. N. Application of machine vision in laser technologies. Trudy MAI, 2022, no 127 The article deals with the problem of applying machine vision methods for practical implementation in the production of modern laser technologies, in particular, selective laser melting technologies. The authors describe the software platform of machine vision created and implemented in production. Examples of the solved problems of machine vision and scientific visualization in the framework of the industrial implementation of new laser technologies are presented. The results of the executed work allowed creating a specialized machine vision platform with possibilities of functions expansion in future that empowers simplifying solution of a wide range of machine vision tasks for the of laser technologies implementation. The problems of object recognition occurring in the process of laser technologies developing were considered. One of the problems of the object recognition in industry has been solved, namely the problem of finding a sheet in the working field of the machinetool. The authors developed and implemented an algorithm for the object contours determining from the previously found angles, which was employed to solve the problem of finding and analyzing the quality of holes while perforation, as well as finding geometry of the fused layer in the process of selective laser melting. The developed software platform for machine vision allows processes recording in isolated environments, the objects boundaries determining in an image, analyzing and processing visual data, forming and presenting a pattern of heat distribution in a threedimensional object. It empowered combining the calculated data on the product geometry and the data, obtained by video data analyzing from visual observation tools, with the data on the heat distribution, obtained as the result of numerical experiment in accordance with the implemented mathematical model of the selective laser melting process under study. The proposed approach allows automating the production control process and simplifying analysis and identification of critical areas for technologists, as well as the technological parameters selection for the process of selective laser melting. The created machine vision software platform has been tested and implemented in the software solutions employed in a number of hightech industrial productions. 
Vatutin M. A., Klyuchnikov A. I. A technique for increasing the stability of the nonlinear link with a delay for the selfoscillating accelerometer. Trudy MAI, 2022, no 127 The article presents the results of applying a scientificmethodological and circuit—engineering approach to the stability improving of acceleration measurements made by serial pendulum accelerometers, primarily micromechanical ones, as well as the results of studies on the stability increasing of the nonlinear link with lagging for the autooscillatory accelerometer. For the nonlinear link operation stability studying, its digital implementation was selected, allowing utterly high operation stability ensuring of the digital part namely. Besides the digital part, an analog comparator is employed in the nonlinear link, which ensures the several orders of magnitude worse operation stability than this of the quartz oscillator. The results of the comparator response time meansquare deviation are presented for the case of its operation in the normal configuration and for the case of application of the amplifier being recommended. The authors show that the additional amplifier implementation reduces the meansquare deviation value of the comparator response time. The study was being conducted by the comparator switching process modeling. Recommendations on the additional amplifier circuitry are given. The article presents specifics of electronic components allowing eliminating comparator in principal, as radio electronic component, form the circuit. The obtained results may be applied to the stability increasing of the accelerometer conversion coefficient and, as the result, determining more accurately parameters of the spacecraft orbit autonomously under conditions of disturbance factors of the outer space. 
Popov I. P. Monoreactive harmonic oscillator. Trudy MAI, 2022, no 126 In classical oscillators, free sinusoidal oscillations are accompanied by an exchange of energy between its elements, which have the opposite nature of reactivity. In a spring pendulum, the potential energy of an elastic element is transformed into the kinetic energy of an inert element and vice versa. These elements have opposite character of reactivity. In an electric oscillatory circuit, the energy of the magnetic field of the coil is transformed into the energy of the electric field of the capacitor and vice versa. These elements also have the opposite character of reactivity. Oscillators are known in which free sinusoidal oscillations are accompanied by the transformation of the kinetic energy of an inert element or the potential energy of an elastic element into the energy of the magnetic field of the coil or the energy of the electric field of the capacitor and vice versa. The synthesis of a monoreactive harmonic oscillator is based on three premises. First. The oscillator consists of two weights of the same weight. Second. Loads make sinusoidal movements. Third. The total energy of the oscillator does not change with time. In a monoreactive (mm) harmonic oscillator, inert elements can perform free sinusoidal oscillations, which are accompanied by the transformation of the kinetic energy of an inert бthe first inert element is zero. In this case, the energy of the second element has a maximum value. At the next moment of time, the first element acquires acceleration due to the kinetic energy of the second element, the speed of which begins to decrease. 
Safonov A. I. On periodic motions of a hamiltonian system with two degrees of freedom in the vicinity of a multiple resonance of the third order. Trudy MAI, 2022, no 126 In this paper, we study the motion of a nonautonomous 2πperiodic in time Hamiltonian system with two degrees of freedom in a neighborhood of a trivial equilibrium that is stable in the linear approximation. It is assumed that the system contains a small parameter ε, and for ε = 0 the Hamiltonian of the system does not depend on time. Let the values of the parameters be close to the resonance values corresponding to the double (fundamental and combination) resonance of the third order. Then, the trivial equilibrium of the complete system is unstable. It is assumed that there is a resonant detuning in one of the frequencies of the linear oscillations of the system. The goal of the paper is to solve the question of the existence, number and stability (in the linear approximation) of periodic motions of the system in a small neighborhood of the origin. Using a number of canonical transformations, the Hamiltonian functions are reduced to the forms that are characteristic for each resonance case. Model systems corresponding to autonomous systems are studied. The parameter space of the problem is divided into regions, and in each region the question of the existence and number of resonance equilibrium positions of the model systems is solved. The results are compared with ones in the case of exact resonance. Using the Sylvester criterion, the sufficient conditions for the stability of the equilibrium positions are verified, and the equilibrium positions satisfying them are found. The characteristic equation of the linearized system of equations of perturbed motion is analyzed, and the necessary conditions for stability of the equilibrium positions are obtained in the form of the system of inequalities The equilibrium positions are found, for which one of these conditions is satisfied; the remaining equilibrium positions are unstable (in the complete model systems) A complete analysis of the necessary conditions for stability has not been carried out due to cumbersomeness. Using the Poincare small parameter method, the periodic motions generated by the considered equilibrium positions are constructed in the complete nonautonomous systems. They are analytic in ε and 12πperiodic in t. The conclusions are drawn about their stability (in the linear approximation) or instability. 
Avdyushkin A. N. On parametric resonance near the libration point L1 of a planar restricted photogravitational threebody problem. Trudy MAI, 2022, no 126 A planar elliptic restricted photogravitational threebody problem is considered, i.e. it is investigated the motion of a lowmass body under the influence of both gravitational forces and light pressure forces acting from two massive bodies that move along known Keplerian orbits. It is assumed that the all three bodies move in the same plane. There is a particular solution in this problem describing the motion, which the lowmass body is located on the segment between the attracting centers at the socalled collinear libration point L_{1}. In this paper, we study the problem of the collinear libration point L_{1} stability in the case of small eccentricity of the massive bodies’ orbits. The system of perturbed motion equations is written in Hamiltonian form. It is established that in this system there are possible both basic and combinational parametric resonances leading to instability L_{1}. The normal form of the Hamiltonian quadratic part of the perturbed motion equations is obtained in explicit form by the method of a small parameter. This made it possible to reduce the linear stability problem L_{1} to the equivalent stability problem of a linear autonomous system with a normalized Hamiltonian. The explicit expressions defining the boundaries of the parametric resonance regions were found on the basis of this autonomous system and it was obtained the stability conditions L_{1} in the linear approximation. Previously, the regions of stability and instability were obtained numerically in [12]. Carried out in that work the numerical analysis results are in good agreement with the results obtained analytically for small values of eccentricity in this article. 
Martirosov M. I., Khomchenko A. V. Computational and experimental study of the behavior of a flat reinforced carbon fiber panel on impact. Trudy MAI, 2022, no 126 Among the structural materials currently used in aviation technology (OT), polymer structural materials (PCM), for example, carbon fiber plastics, which have certain advantages over traditional metal materials for structural purposes, have become widespread. Among such advantages are relatively low density, high specific strength and rigidity, high wear resistance, fatigue resistance, low coefficient of thermal expansion, resistance to chemical aggressive media, damping ability. Speaking about the disadvantages of PCM, it should be noted that during the production and operation of structural elements made of such materials, defects of various types may occur, which have a serious impact on the residual strength. The level of safety of an AT created on the basis of new materials and new technologies should not be lower than the level of safety of an existing AT made of traditional structural materials (and according to traditional technologies). It is important to note that the purpose of developing new PCM is to combine various components to create materials with new specified characteristics that differ from the characteristics of the original components. In the works [1][4], the behavior of structural elements made of PCM in the presence of multiple defects such as bundles of arbitrary shape, size and location under the action of nonstationary loads of various nature was previously considered. The paper presents a numerical and experimental study of the behavior of a fourstringer flat panel made of a polymer composite material under lowspeed impact. Validation of the numerical experiment based on the results of field tests was carried out. The validation results showed that the maximum stratification area as a result of the impact differs by no more than 11%. 
Yu Z. ., Temnov A. N. Equivalent mechanical model of liquid linear sloshing under microgravity. Trudy MAI, 2022, no 126 A numerical approach to develop the equivalent mechanical models representing liquid sloshing is established and the effects of surface tension are taken into account which are predominant in lowgravity environment. An appropriate model is a pendulum that has a mass which represents the liquid fraction that participates in the fundamental model of the sloshing. Furthermore, the pendulum must be attached to the tank through a torsional spring which represents the stiffening effect of surface tension. A formulation is derived from the linearization of the motion equations of the liquid near its initial equilibrium position considering pressure jump on the free surface and freeend boundary condition at the threephase contact line. The continuous problem domain is discretized by the finite element method and its discretization gives a classical generalized eigenvalue problem, whose solutions are natural frequencies and mode shapes. Expressions for the parameters of the mechanical model are obtained by the principle of dynamic similarity. Several examples illustrate the influence of Bond number and fill levels on the behavior of liquid in toroidal tanks. Comparing numerical results with the experimental measurements obtained under ground conditions, it is found that the nondimensional eigenvalue and slosh masses increases as Bond number increases, but the spring moment and length of pendulum decreases. The results obtained in this paper can be used in the coupling dynamic analysis of the spacecraft with propellant tanks. 
Kutysh I. I. New methods for constructing uniformly convergent trigonometric Fourier series. Trudy MAI, 2022, no 126 New results of studies of convergence of trigonometric Fourier series (TFS) with Fourier coefficients constructed by various methods are presented. Using the concept of the square of the relative norm, the possibility of an analytical representation of a given TFS function is analyzed in detail and it is established that the cause of the divergence of the TFS with a sufficient increase in its degree is the occurrence of the Gibbs effect. It is shown that when assessing the convergence of the TFS to its function as an independent change of the relative norm, instead of the current value of the degree of the series k, it is reasonable to use the current value of the generalized variable Θ=kπ/n, which allows us to obtain more general results. Moreover, it is sufficient to control only the value of Θ, which determines the amount of calculations. Recommendations are given for the construction of such Fourier coefficients that ensure uniform convergence of the TFS to its functions f(x) and the correct finding of their first derivatives free of the Gibbs effect. Uniformly convergent TFSs constructed according to the proposed method are compared with the known Filon and Lanczos series. In contrast to the Lanczos method, it is proposed to use variables σmultipliers depending on the new variable ζ, which affects the rate of convergence of the series to its function f(x) and the accuracy of determining the first derivatives of the series without the occurrence of the Gibbs effect. The results on the construction of uniformly convergent TFSs relate to any maximumnormalized periodic function f(x) in the interval [π, π] satisfying Dirichlet conditions. Moreover, if the function f(x) has zeros at the ends of a given interval, then it is advisable to build a shortened TFS with decomposition only in terms of sinuses, hence a simpler TFS. The proposed uniformly converging TFSs can find application in solving various problems of gas dynamics and heat and mass transfer described by partial differential equations. 
Averyanov I. O., Zinin A. V. The use of RodriguesHamilton parameters in mathematical model of cargo landing system with dampers in tasks of its overturn. Trudy MAI, 2022, no 126 In the previous article [1] we described the mathematical model of dynamic landing process for cargo dropped systems with dampers (System) that we developed for statistical modelling of the process. That dynamic model consisted of spatial equations of forces and moments equilibrium, kinematic Euler’s equations and contained contact boundaries from rigid plane to dampers and to cargo. The method of forth integration was used to solve the equations and the idea was that such modeling of landing process had allowed us to detect all the failures well known for such Systems. One of the possible System failure that may occur during landing is its overturn. In this case we have a deal with large angles that may lead to problems with kinematic Euler’s equations. Researching of sources shows that the problem of System overturn usually considers separately with analytical approaches, while the method we used implies continuity of the solution from the beginning of the process to its end. To avoid such problems in this article we consider the use of RodriguesHamilton parameters (or quaternion) instead of kinematic Euler’s equations to solve the dynamic task of complex System moving. We use the fourth order of RungeKutta method to realize the algorithm of RodriguesHamilton parameters. To convert the quaternion to spatial angles Krilov’s equations are used. To demonstrate accuracy and stability of the developed algorithm the task of complex rigid body spatial free motion is considered. Comparison of these results with the solution that comes from commonly used CAE shows us their similarity. After that, we also consider the task of System landing with its overturn. These results are considered from qualitative analysis point of view. Thus, the use of algorithm we realized with RodriguesHamilton parameters instead of kinematic Euler’s equation in the mathematical model of System landing process allows us to avoid «special points» and to generalize the solution to the tasks of large spatial angles, including System overturn. 
Lebedev E. L., Repin A. O. Method of acoustic emission control of the contact interaction of rolling bearing elements when evaluating the correctness of the resource assembly of ball bearing supports as a tribological system of power gyroscopes rotors. Trudy MAI, 2022, no 126 The autonomous functioning of the power gyroscopic complexes of small spacecraft does not allow maintenance during its operation. One of the most loaded elements of the power gyroscope are rolling bearings. Since the functioning of rolling bearings depends on the correctness of their assembly and the presence of lubrication, in order to ensure the autonomous functioning of the rotors of power gyroscopic systems, the technology of resource lubrication and resource assembly of the bearing assembly is used in their manufacture, which implies onetime lubrication and assembly (without the possibility of adjustment) for the entire life of the device. The article presents the results of research on the use of a method for quality control of assembly of ball bearing bearings of power gyroscopic complexes operating in vacuum space by estimating the size of the bearing clearance by the parameters of acoustic emission signals. The definition of the limiting state of the bearing supports of the rotors of power gyroscopic systems is given, by which it is necessary to understand the state when the friction losses of the bearing (taking into account the progressive heat release) will exceed the difference between the maximum torque generated by the electric motor of the rotor of the power gyroscope and the torque necessary to ensure the required angular velocity of the rotor flywheel, taking into account its moment of inertia. It is proved that the main criterion for the correctness of the resource assembly of a ball bearing assembly is to ensure the correct contact interaction of its elements as a tribological system. At the same time, the main controlled parameters are the force that the bearing perceives after the rotor assembly, as well as the parameters of elastic deformation in the ball—ring bearing system. A model of natural frequencies of elements of bearing supports of power gyroscopic systems has been developed taking into account their stressstrain state. The dependence of the frequency of natural oscillations of the bearing ball on the force acting on the bearing after its assembly is proved. This dependence is of a powerlaw nature and can be used in the development of a new method of quality control of the resource assembly of bearing supports of power gyroscopes. 
Goncharov P. S., Kopeyka A. L., Babin A. M. Method for experimental modeling of the effect of plasma radiation from an electric rocket engine on solar cells. Trudy MAI, 2022, no 126 The article presents a technique for experimental modeling of the impact of plasma radiation from an electric rocket engine on solar cells. The used laboratoryexperimental base and the procedure for conducting tests are described. Relationships for calculating the coefficients of degradation of the electrical characteristics of solar cells are given. The essence of the approach of experimental modeling of the effect of plasma radiation from an electric rocket engine on solar cells is to measure: the temperature field of a solar cell, the characteristics of the plasma flow, the electrical characteristics of solar cells before and after exposure to the plasma radiation of an electric rocket engine, and to calculate the degradation coefficients of solar cells. It is advisable to use the obtained values of the degradation coefficients in the design of spacecraft solar arrays. The presented technique makes it possible to determine the coefficients of degradation of the electrical characteristics of solar cells when exposed to plasma radiation from an electric rocket engine, as well as to carry out studies: — on the influence of the effect of plasma radiation from an electric rocket engine on the electrical characteristics of solar cells, depending on the parameters and modes of operation of an electric rocket engine; — on issues of increasing the energy efficiency of an electric rocket engine by using the energy of plasma radiation by returning it to the onboard network using photoelectric or thermal converters. The multiplicative degradation coefficient determined in the course of tests allows one to perform an estimated calculation of the power generated by a solar cell after exposure to plasma radiation from an electric rocket engine. 
Sha M. ., Sun Y. . Experimental study of damage to the structure of composite materials of highspeed aircraft from raindrop impact erosion. Trudy MAI, 2022, no 126 Bodies moving at very high speeds through a rainfield can experience severe damage caused by the impingement of raindrops on their surfaces. This effect is usually referred to as"rain erosion". Rain erosion has been a concern of the aviation industries for many decades, and rain erosion resistance is one extremely important parameter of the interaction of materials with the flight environment. In this paper, a single waterjet impact test platform was established based on the firststage light gas gun in order to conduct the rain erosion tests on materials. Its principle was that the gas gun launches a metallic projectile to impact the water storage chamber sealed by the rubber piston, and then the liquid was driven from the small nozzle to form a highspeed waterjet. The apparatus could generate stable waterjets with speeds of 200−600 m/s, diameters of 4−7 mm and a smooth circulararc head, which simulated a waterdrop with the same diameter. A series of single waterjet impact tests were carried out on a symmetrically crossply carbonfiberreinforced composite (CFRP) laminate under different waterjet velocities and diameters. The results show that the typical damage modes of CFRP laminates impacted by single waterjets are as follows. The impacted surface is depressed, and the surface damage consists of resin removal, matrix cracking, minor fiber fracture and fiber exposure around the rim of a central undamaged region. The internal damage range gradually expands from the impact surface to the bottom ply, mainly composed of intralaminar matrix cracking with a pyramid shape and interlaminar delamination with a diamond shape. Both the surface and internal damage are more extensive in the longitudinal than the transversal direction, thus presenting typical. 
Sedel'nikov A. V., Orlov D. I., Serdakova V. V., Nikolaeva A. S. Investigation of disturbances from a temperature shock of a solar battery panel when simulating the rotational motion of a small spacecraft around the center of mass. Trudy MAI, 2022, no 126 The main goal of the work is to evaluate the effect of the solar battery panel temperature deformations when a small spacecraft leaves the Earth’s shadow on the parameters of its rotational motion. The problem lies in the transformation of a small spacecraft after the end of its active existence into space debris, which significantly complicates the successful implementation of new space projects due to the threat of collision. Currently, many methods have been developed for cleaning up space debris. One way involves towing space debris using tether systems. At the same time, the connection between the tug and space debris is not sufficiently reliable so the cable can separate from space debris under the influence of various disturbances. One of such disturbances may be a temperature shock of the solar panel when the space debris is a small spacecraft with large elastic structural elements. The greater the mass fraction of the elastic element in the total mass of a small spacecraft, the more significant the effect of the temperature shock on the dynamics of its rotational motion. An analysis of research by scientists from around the world shows that the temperature shock can disrupt favorable conditions for the implementation of gravitysensitive technological processes, causing temperature fluctuations in large elastic elements, which lead to unacceptably high microaccelerations. During experiments on the International Space Station with promising solar panels of the ROSA type, temperature fluctuations were so intense that they did not allow the panels to be rolled up at the end of the experiment. In this case, the question of the controllability of a small spacecraft equipped with such solar panels already arises. The article deals with issues related to the influence of angular acceleration from the temperature shock and a disturbing factor on the functioning of the spacecraft. The influence of angular acceleration from the temperature shock is estimated on the basis of numerical modeling and construction of the deflection field of the plate median surface as a result of the temperature shock in the ANSYS software. For the small «Starlink» spacecraft, the values of the angular acceleration from the temperature shock and the deflection field of the plate middle surface as a result of the temperature shock were obtained. As a result of the research, the dependence of the angular acceleration on the temperature shock of the small «Starlink» spacecraft was obtained and the maximum value of the disturbing moment was estimated. When transporting such a small spacecraft using tether systems after the end of its active life, this disturbance must be taken into account in order to avoid the contact loss between the tether and space debris as a result of temperature shock. The results obtained can be used to analyze the possibilities of transporting space debris using tether systems. 
Polyakov P. O., Shesterkin P. S. Numerical modeling of damping coatings. Trudy MAI, 2022, no 126 In various industrial sectors, damping materials are used that are suitable in their properties for specific working conditions. The use of damping tapes is one of the existing ways to improve the damping properties of materials. At the moment, for modern thinwalled structures, there is a need to develop more advanced calculation models, for which the actual operating conditions of structures should be sufficiently fully reflected, taking into account the mechanical properties of the material from which its elements are made. The damping properties of the materials from which they are made, as well as the amplitudes of their oscillations, have a significant impact on the dynamic tension of the elements of thinwalled structures. Improving damping properties is one of the methods to increase the service life of structural elements subject to cyclic loading during operation. To damp vibrations in different frequency ranges that occur under external influence, as well as on the weight characteristics of the system, the choice of optimal types of damping coatings depends. This article explores the effect of 3M brand damping tape on the dynamic characteristics of a cantilever beam and the simulation of this process. and modeling of this process. The results of numerical simulation of free vibrations of an aluminum beamplate without damping layers and with damping tapes glued to the front surfaces (threelayer beams) are presented. For numerical simulation of models of plates of all investigated sizes with a damping tape, simulation of the oscillatory process was applied similarly to physical testing. A finite element model of a plate with a grid is constructed. The dynamic characteristics of threelayer beams are determined. The dependence of the change in the damping coefficient on the amplitude for samples with and without damping tapes for different amplitudes is established, the amplitudefrequency characteristic, the logarithmic damping decrement, the damping coefficient and the natural frequency of the samples without a damping layer and with its participation are obtained. Numerical modeling was carried out in order to compare the experimental results of the dynamic characteristics of a cantilever beam without and with a damping layer. 
Dinyaeva N. S., Kravtsov S. B., Krumlyakov S. O., Benkalyuk G. A. Numerical modeling of damping coatings. Trudy MAI, 2022, no 126 The paper considers the development of a special device  a stand for filling flat heat pipes with a liquid coolant, as well as a method for filling them, based on controlled flow under the influence of gravity of the coolant in the internal space of heat pipes (HPs). The coolant (coolant) used for pouring into heat pipes is pretreated — dissolved gases are removed from it. The degassing of the coolant is carried out in order to minimize the process of oxidation of the internal metal parts of the case and the evaporative capillaryporous structure (ECS) of the HP. In order to increase the efficiency of the process of filling experimental batches of heat pipes, reduce material and time costs, a special device is proposed  a filling stand that combines all technological operations that were carried out separately into a single technological cycle. Degassing is carried out by ultrasonic (US) cavitation in a special container installed in an ultrasonic bath, which is an integral part of the filling stand. The implementation of this development allows you to get a useful result, which consists in:  saving labor costs by reducing the number of technological operations and design features of the installation;  increasing the reliability of HP sealing associated with the possibility of visual control over the entire technological cycle of refueling;  an increase in the depth of coolant degassing, which in turn affects the extension of the service life of filled HP;  reducing the probability of failure of the radar by increasing the reliability of the cooling system PPM AFAR;  possibility of production in a short time of pilot batches of HP for further research. 
Bakhtin A. A., Volkov A. S., Solodkov A. V., Eletskikh E. V. A research of influence of clipping on OFDM system performance. Trudy MAI, 2022, no 126 
Khazov A. S., Ortikov M. Y., Gusev S. N. A method for estimating the resolution of a space radar with a synthesized antenna aperture, taking into account the compensation of atmospheric distortions. Trudy MAI, 2022, no 126 The article proposes the methodical approach allowing to solve a problem of improvement of quality of the radar images received by space synthetic aperture radar radars from the antenna synthesized by an aperture due to accounting of atmospheric distortions. The purpose of work is improvement of approaches to formation of radar images. Object of research are methods of estimation of resolution of the s space synthetic aperture radar which is used as the key information indicator and characterizes detail and quality of radar images. The result of the work is a the technique of estimation of resolution of the space synthetic aperture radar taking into account compensation of atmospheric distortions. The proposed technique is based on the use of compensation of atmospheric distortions from positions of geometrical optics. The offered technique of estimation of resolution of the space synthetic aperture radar allows to determine the amendment to inclined range taking into account the joint impact of distortions of the troposphere and an ionosphere at a stage of formation of basic function by an azimuth in synthesis algorithms of radar images. Accounting of a refraction of electromagnetic waves and correction of inclined range are realized with use of index of refraction of the environment and a method of approach of geometrical optics at distribution of radio waves in the nonuniform environment. For use of this approach it is necessary to define a condition of the atmosphere with use of models of the troposphere and an ionosphere in a zone of the review of the synthetic aperture radar taking into account real geophysical conditions. Results of imitating modeling confirm a possibility of use of the proposed technique for estimation and accounting of the errors brought by the atmosphere of Earth in measurements of radar parameters by means of methods of calculation of trajectories of radio waves at the set index of refraction of the environment. The developed technique allows to carry out compensation of impact of atmospheric distortions and to increase quality of the received radar image. The proposed methodical approach can be used for performing synthesis of radar images, for elimination of errors of measurement of coordinates of objects and for improvement of values of resolution and contrast of radar images. 
Detkov A. N. Optimal discrete filtering of samples of a continuous random process against the background of correlated Markov noise. Trudy MAI, 2022, no 126 In modern onboard informationmeasuring systems (IMS) of UAV, algorithms for optimal or quasioptimal processing of random processes are practically implemented using digital signal processing tools. Therefore, these algorithms must be synthesized in a discrete form in the form of recurrent relations that are convenient for such an implementation. However, in most cases, the mathematical models of the processes evaluated and observed in the IMS have a continuous form of recording, which is due to the physical nature of the phenomena occurring with the signals. In this regard, the problem of synthesizing optimal algorithms for discrete filtering of counts of continuous random processes arises. At the same time, the modern element base makes it possible to use a high sampling rate in onboard IMS, which leads to autocorrelation of measurement readings. Therefore, in the statistical synthesis of filters, it is necessary to take into account the correlation of measurement noise, which significantly affects the generated filtering estimates. In this paper, proposes a new discrete Kalman filter (KF) based on a statistically equivalent discrete representation of continuous state and observation vector models to solve the problem of optimal linear filtering of samples of a continuous vector Markov random process, taking into account the known statistical characteristics of additive vector Markov correlated noise. The problem of filtering a statespace linear model with colored measurement noise and precise noise covariance matrices is converted to a problem of estimating a statespace linear model with white Gaussian measurement noise and precise noise covariance matrices using the measurement difference method and without state vector augmentation. The structure of analogtodigital conversion and discrete KF is presented. The main feature of this algorithm is the accumulation (integration) of continuous observation on the time intervals between adjacent samples of the estimated state vector. To illustrate the potential characteristics of the accuracy and noise immunity of the synthesized algorithm, a simple example of filtering a continuous Gaussian Markov random process against the background of Markov random noise is considered. From the graphs presented, one can quantify how much analog and discrete algorithms for optimal filtering of a continuous random process depend on the ratio of the width of the spectral density of the measurement noise to the width of the spectral density of the random process and the signaltonoise ratio. The presented discrete filtering algorithm allows us to quantify the deterioration of the potential characteristics of accuracy and noise immunity in the case of optimal estimation of continuous random processes due to the coloration of measurement and sampling noise. The use of the method of difference measurements does not increase the computational costs in the discrete KF, since the dimension of the state vector remains unchanged, as in the case of filtering continuous random processes against the background of white Gaussian noise. At the same time, the analog part of the analogtodigital converter is significantly simplified in comparison with similar algorithms, since a onecycle delay is implemented in a discrete KF after the ADC. It should also be noted that there is no operation of analog differentiation inherent in classical algorithms for filtering continuous random processes in continuous time using the method of difference measurements. 
Ibragimov D. N., Berendakova A. V. Method of constructing and estimating asymptotic controllability sets of twodimensional linear discrete systems with limited control. Trudy MAI, 2022, no 126 
Pavlov A. N., Umarov A. B., Kulakov A. Y., Gordeev A. V. The problem of planning the reconfiguration of the motion control system of a small space vehicle for remote Earth sensing under the conditions of the unknown cyclogram of its functioning. Trudy MAI, 2022, no 126 Of particular importance at the present time in the development and operation of small spacecraft are the issues of ensuring the required degree of autonomy and survivability, as well as increasing the efficiency of the small spacecraft in various environmental conditions. The relevance of solving these problems for small observation spacecraft is caused, on the one hand, by the peculiarities of the orbit on which this type of spacecraft operates, and on the other hand, by the lack of the possibility of timely control in the event of emergency situations on board the small spacecraft. To ensure the autonomy and survivability of a small spacecraft, it is necessary that it be in working condition for a maximum time or quickly restore its working capacity. That is, it is necessary to be able to change (rebuild) the structure (structures) of the small spacecraft in various environmental conditions in order to maintain the required level of performance. In practice, when solving problems of ensuring reliability, survivability, disaster tolerance and fault tolerance of complex technical systems within the framework of the currently developed theory of structural dynamics control, such a variant of managing the structures of a complex technical object as reconfiguration has become widespread. This article proposes a method for solving the problem of planning the reconfiguration of a complex technical object based on structural and functional reconfiguration under the conditions of an unknown cyclogram of the activation of the complex technical object operating modes. A computational experiment was carried out on the example of a small spacecraft for remote sensing of the Earth «Aist2D». 
Sokolova Y. V., Leun E. V., Primakov P. V., Samoylov S. Y. Approach to planning the load of processors of critical multiprocessor systems. Trudy MAI, 2022, no 126 One of the priority areas in economically developed countries is the security of critically important, especially complexly organized systems. Examples of such systems are a variety of robotic production; nuclear power plant control systems; onboard computing systems; groups of unmanned aerial, land and water robots; global navigation satellite system (GLONASS); large software systems of high importance and many other systems. The main problem of building computing systems at all times remains the task of ensuring their longterm functioning. This task has three components: reliability, availability and serviceability. Of particular relevance is the use of computer systems for managing critical objects operating in real time. The main difference between realtime operating systems and any other operating systems is the guarantees for the start or end time of processes that are provided by realtime systems. In the event of a failure, such systems are subject to high requirements for operability, nonfailure operation, safety, security, etc. Obviously, the most important thing is to minimize the time and hardware costs required for the response of a multiprocessor system to an emergency situation. One of the options for solving this issue may be planning the load of processors in multiprocessor systems. In this case, you can avoid simultaneous loading of several processors by one task (program, subroutine, algorithm, file, etc.) and, at the same time, schedule the queue of incoming tasks in such a way that they are served simultaneously. This allows you to reduce unplanned downtime and at the same time increase its availability along with increased speed. The article is devoted to multiprocessor systems. The issue of compiling a plan for loading processors in them is touched upon. It is supposed to use the socalled realtime systems. 
Mokhov A. I., Kislinskiy V. G., Alekseychuk A. S. Session based recommender system with multistage candidate sampling. Trudy MAI, 2022, no 126 Understanding users’ preferences is a challenging task especially with a huge amount of items. Modern recommender systems are keen to solve this task by applying stateoftheart methods of candidate sampling and simple heuristics in couple with Machine Learning ranking algorithms. This paper presents an algorithm of candidate sampling from three different sources followed by a ranking algorithm. These two stages form a sessionbased recommender system that is capable of building a user’s probable preferences based on its current session. For candidate sampling, we use a language model (Word2Vec) and sparse vectors for item representations, and the most popular items from a dataset. Each stage is divided into multiple substages making it really simple to add new candidate sources or remove existing ones. The same technique can be easily applied to ranking algorithms — one can remove a ranking algorithm or add the new one in order to blend model predictions maximizing Precision or Recall metrics as well. We also show the importance of ranking algorithms in recommender systems by measuring Learning to Rank (L2R) specific metrics on test data. There are several ranking algorithms in this paper. All of them belong to the pairwise algorithms subclass. Such algorithms as LambdaRank, YetiRank, and StochasticRank are used in comparison to nonranked recommendations. We use CatBoost implementation of gradient boosting and PyTorch to build a neural ranking net. As a result of the experiment, we get a ready endtoend recommender system pipeline with flexible modules that are easy to add/remove and show the benefits of ranking models with recommendations on real data. 
Deniskina G. Y. CAD/CAM/CAE system for manufacturing structures from fibrous composite materials using 3Dprinting. Trudy MAI, 2022, no 126 The problem of development and implementation of a CAD/CAM/CAE system for manufacturing structures from fibrous composite materials using 3D printing is considered. The general configuration of the system and the assignment of its functional modules are described. The advantages of the mathematical support and software developed for the system for creating digital twins, which allow generating control programs and conducting virtual modeling of a 3D printing process to be used in the manufacture of products of complex geometric shapes, as well as developing rational schemes for the reinforcement of printed composite structures and finding optimal printing modes, are shown. CAD/CAE system is focused on modeling, visualization of the placement of fibers in the printing area, finding the optimal printing scheme based on the requirements conditioned by the product operating conditions. In this connection, it must meet the following requirements:
The main principles of development of a CAD/CAM/CAE system for manufacturing functional structures from fibrous composite materials using 3D printing are considered. The task of modeling and visualization of the 3D printing process is formulated. The main specifications of the developed CAD/CAM/CAE system associated with the possibility to set the structure of a facility with its subsequent adjustment and smoothing. triangulation of the print area and modeling of placement of fibers using analytical functions during the printing process are determined. Mathematical tools for solving equations characterizing mechanical properties of composite materials based on wavelet analysis methods, as well as for calculating the optimal directions for placing fibers of composite materials are described. 
Budaev G. A., Danilov D. A., Konotop O. I. Numerical calculation of the flap Tgearbox kinematic error. Trudy MAI, 2022, no 126 This article is devoted to research of the kinematic error in the units of servo systems with mechanical transmissions. The flap Тgearbox of the high lift transmission was considered as the object of the study. Numerical simulation methods were used to determine the kinematic accuracy of the research object. Geometric dimensioning and tolerances of gearbox components were assigned, a 3D CAD model was built with the worstcase combination of tolerance fields, material characteristics were assigned, forces, constraints and boundary conditions were specified, and the results were evaluated. There are many methods of solving this issue. Analytical methods and methods using 3D modeling allow to determine the kinematic error in the early stages of the design, but they are not automatized. Experimental methods of calculation have the greatest accuracy, but are not possible in the early stages of project development. The numerical simulation method is devoid of the disadvantages of analytical methods. The basic equation of dynamics for the investigated system was formulated and solved using the HHT integrator based on the αmethod. The interface between the surfaces of the rigid bodies was defined by contact force. In the first case of the calculation, the gearbox housing was fixed in space, the other bodies were constrained to move in a plane perpendicular to the plane of rotation of the shafts. In the second case, only the outer rings of the bearings and their sleeves were constrained to move in the plane, because they were fixed in the axial direction in the real construction. Because of the shaft axis displacement possibility in angular directions and the possibility of axial displacement, the kinematic error increased significantly. At the early stage of development, the value of gearbox kinematic accuracy was determined. The obtained value complies with the requirements for the accuracy of the high lift transmission. The specified geometric dimensioning and tolerances are not very precise or too rough and can be applied to other single stage bevel gearboxes used in high lift transmissions. 
Golyakov A. D., Richnyak A. M., Fominov I. V. Investigation of the accuracy parameters of a spacecraft with an adaptive autonomous navigation system. Trudy MAI, 2022, no 126 The paper presents the results of solving the scientific problem of synthesizing an adaptive autonomous navigation system of a spacecraft and presents the results of a study of the accuracy of determining the navigation parameters of a spacecraft under the influence of disturbing factors that can be continuous, periodic and shortterm. Their manifestation is difficult to predict. The impact of disturbing factors on the onboard equipment can lead to both a gradual and a sharp decrease in the effectiveness of spacecraft target tasks due to the deterioration of technical characteristics of optical elements of star sensors, external optical elements of navigation devices, temperatureregulating coatings and electronic equipment of the autonomous navigation system, which, in turn, can cause a metrological failure of onboard measuring instrument devices. To estimate measurement errors of navigation parameters of the spacecraft, an algorithm for the operation of an autonomous navigation system has been adopted, where the zenith distances of two navigation stars and the altitude of the spacecraft above the Earth’s surface are used as primary navigation information. Simulation results are presented for the case when measurements of onboard measuring instruments contain random errors distributed exponentially. It has been shown that the disturbing factors of the outer space lead to an increase in characteristics of random errors of onboard measuring instruments and, as a consequence, to an increase in spacecraft navigation errors. The study has been carried out by modeling the process of solving the navigation problem, taking into account the impact of disturbing factors navigation parameter onboard measuring instruments. The basis for obtaining numerical estimates of the accuracy of the spacecraft autonomous navigation system is the simulation of the process of solving the navigation problem using computer technology. To process the results of navigation measurements containing unavoidable random errors, a nonrecurrent weighted least squares method has been used in the work. The obtained results can be used to counteract disturbing factors of the outer space that reduce the accuracy of the spacecraft navigation and to justify adaptive and reconfigurable systems that allow autonomously to determine the parameters of the spacecraft orbit in the conditions of disturbing factors of the outer space. 
Minakov E. P., Aleksandrov M. A., Verbin A. V. Algorithms for estimating the number of lunar asteroid detection tools with a vertical orientation of the sight axes. Trudy MAI, 2022, no 126 Due to the peculiarities of the orbital movement of asteroids approaching the Earth, a significant proportion of them either in principle cannot be detected using existing monitoring tools located on the surface of the Earth, or detection can occur too late. The lack of influence of the atmosphere on optical observation means leads to the advantages of the location of asteroid detection means in space. In this article, a study is carried out on one of the possible ways of their stationary location — uniform distribution with regard to visibility zones on the surface of the moon. An algorithm is proposed, which allows on the basis of initial data on the angle of solution and the maximum range of detection of dangerous space objects by lunar means. The zone of near and longrange explosive detection, as well as the zone of continuous multiple detection of asteroids, their description and illustrations are given. Computational experiments were carried out using the developed algorithm for estimating the number of means for detecting asteroids when placing on the entire surface of the Moon or its part, dependencies of the angular distance between the standing points and the angular dimensions of the visibility zones of the means for detecting asteroids on the maximum range of detecting asteroids were obtained. In addition, an algorithm was developed and the number of means for detecting asteroids with vertical orientation of the sighting axes was estimated with the exception of a part of the Lunar Surface for their placement, due to the closure of the outer space region by the Earth («dead zone» of asteroid detection means), when placed on the entire surface of the Moon or its part, the dependence of the angular distance between the standing points and the angular dimensions of the visibility zones of the asteroid detection means on the maximum detection range of asteroids is also obtained. The presented algorithms for estimating the angular distance between the points of standing on the surface of the Moon of the same type of asteroid detection means with vertical orientation of the sighting axes and their number for forming the asteroid detection line allow obtaining correct results and can be used for further research to determine the parameters of the asteroid detection line zones, reduce the number of asteroid detection means and estimate the probability of asteroid detection. 
Javadov N. H., Aslanova A. B. Optimization of the use of hybrid multirotor drones for atmospheric research in vertical takeoff mode. Trudy MAI, 2022, no 126 With the advent of drones, it became possible to use unmanned aerial devices to study the pollution of the atmosphere with aerosol, various gases and water vapors. For these purposes, the method of radiometric probes operating in vertical lift mode is still widely used. At the same time, the successful performance of this function with the help of UAVs depends on a number of factors, one of which is the limited time of their flight. For example, the typical flight time of multirotor batterypowered drones is 2050 minutes. One of the ways to solve this problem is the use of a hybrid hydrogen fuel cell (FCHS) system containing a fuel cell and an electric battery The question of using a drone equipped with a hydrogen cell of a hybrid power supply system and electric batteries to study the vertical profile of the atmosphere has been investigated. The problem of finding the optimal dependences of the energy of the power supply system and the power consumption on the altitude is solved, at which, taking into account the limitation on the average height of the power consumption, the flight time can be minimized. This minimization of flight time is explained by the need to eliminate the influence of changes in the atmosphere on the overall result of the study of the structure of the atmosphere. Taking into account the obtained solution, as well as the known dependence of the drone’s power consumption on mass, acceleration of free fall, air density and the area of the propeller disk, a formula for calculating the mass in the optimal mode is obtained. It is shown that in the optimal mode, the condition of mass constancy is provided if the energy of the power supply system increases exponentially. In the absence of such growth, the discharge mode of spent batteries is recommended for the implementation of the described optimal flight mode. 
Huseynov H. A., Zulfugarli P. R., Abdurrakhmanova I. H. On the accuracy of direct georeferentiation of uavs in areas with different climatic conditions. Trudy MAI, 2022, no 126 The tasks of carrying out measurements with relatively high temporal and spatial resolution using UAVs can be successfully performed when carrying out accurate georeferentiation of their position, i.e. linking photogrammetric devices to any coordinate system. There are indirect and direct georeferentiation. With indirect georeferencing, the real coordinates of ground control points (GCP) are taken into account and they are compared with the measurement results of these points in the images. With direct georeferentiation, the direct use of known objects in the image is carried out. An unambiguous determination of the optimal density of GCP placement in RTK GPS systems does not seem to be justified, since the total influence of both technical factors and meteorological factors (water vapor, pressure, temperature) is taken into account. This article suggests a way to account for the influence of such a common factor. The definition of such a generalized factor and the assumption that the magnitude of this factor is not constant in space allows us to formulate and solve the optimization problem of calculating the optimal dependence of the GCP placement density on the specified generalized indicator. The accuracy of direct georeferencing of UAVs in zones with different climatic conditions is analyzed. The optimization problem of finding such indicators of georeferentiation of measuring instruments in x and y as the density of GCP placement (control points) and the pedestal of exponential dependence of the error of georeferentiation on the number of established control points is formulated and solved. It is shown that if we assume the presence of an analytical dependence of the number of control points along the flight path on the value of the specified pedestal, then the minimum of the average integral value of the relative error of referencing is achieved with the presence of an inverse logarithmic dependence of the number of control points on the height of the abovemarked pedestal. 
Barkova M. E. On the issue of constructing a spacecraft route for the disposal of space debris and a space debris object. Trudy MAI, 2022, no 125 The article is a continuation of research published in issue No. 110 of the Proceedings of the MAI and AIP Conference Proceedings 2318, 020009 (2021). The research is devoted to the rendezvous of a space debris disposal spacecraft (hereinafter SDC — space debris collector) with a space debris object for the purpose of capture and processing into fuel. The main problem of the article is a graphical evaluation of the study performed earlier. The purpose of this work is a graphical assessment of the approach of the SCM and the selected space debris object by constructing their paths. The relevance of this work is to increase the number of space debris objects that can damage spacecraft in a collision. According to space debris data provided by the European Space Agency, the number of debris objects is as follows: — 36,500 space debris objects larger than 10 cm; — 1 million space debris objects ranging in size from more than 1 cm to 10 cm; — 130 million space debris objects ranging in size from more than 1 mm to 1 cm. The author concludes that the amount of space debris decreases slowly and only during periods when its formation is small and there is no particularly strong fragmentation. The probability of a spacecraft colliding with space debris increases at orbital altitudes of 800 — 950 km. In satellite orbit, you can see that the disturbing forces and additional masses from the collected space debris had little effect only in small periods. 
Popov I. P. Mechanical analogue of cyclotron motion. Trudy MAI, 2022, no 125 The purpose of the work is to find a mechanical analogue of cyclotron motion and to determine the scheme of the corresponding device, which is appropriate to call a stabilized rotator. The topic of speed stabilization is relevant. From the key circumstance that determines the possibility of generalizing cyclotron motion to mechanics, which consists in the fact that the Lagrangian of an electron is twice as large as its kinetic energy, which, as applied to a stabilized rotator, should be interpreted as the equality of kinetic and potential energies, it follows that the composition of a stabilized rotator should include elements , which are able to store both of these types of energy, namely, the load and the spring. The natural frequency of rotation of a stabilized rotator is strictly fixed (it does not depend on either the moment of inertia or the moment of momentum) and remarkably coincides with the natural frequency of oscillations of a pendulum with identical parameters. When the angular momentum changes, the radius and tangential velocity change (the rotation frequency does not change and is equal to its own). At zero torque in the stationary mode, the rotational speed of the stabilized rotator cannot be arbitrary and takes on a single value. A stabilized rotator can be used to control the natural frequency of a radial oscillator, although in this capacity it may have strong competition from mechatronic systems. On the contrary, as a rotation stabilizer, its competitive capabilities are undeniable and are determined by the extreme simplicity of the design. 
Bairamov F. D., Bairamov B. F. Optimal stabilization of operation of liquidpropellant rocket engine. Trudy MAI, 2022, no 125 The Lyapunov function method is applied to solve the problem on optimal stabilization of the steadystate mode of operation of the twocomponent liquidpropellant rocket engine with turbodriven pump assembly by regulating the pressures in the oxidizer and fuel tanks with considering wave processes in the flow lines. Liquidpropellant rocket engine is a complex mechanical system containing two distributed links and finitedimensional links located at both endpoints of the distributed links. The linearized equations of dynamics of separate links are drawn up. After an exception of some variables from these equations system of dynamic equations of liquidpropellant rocket engine in general have been obtained. To solve the problem on stabilization, first, the Lyapunov function method is used to determine the set of controls (laws for regulating the pressures in tanks) ensuring asymptotic stability of liquidpropellant rocket engine operation. Then, the optimal control is determined on this set by the Lagrange function method from the condition for minimum of the norm at each moment of time. Based on specific equations, the Lyapunov function is constructed as the sum of integral and ordinary quadratic forms, the signdefiniteness of which is checked by the Sylvester criterion. The developed control laws can be implemented quite simply and accurately in practice. It is not possible to ensure the asymptotic stability of liquidpropellant rocket engine operation without regulating the pressures in the tanks. The liquidpropellant rocket engine belongs to the class of systems with distributed and lumped parameters, described by linear equations in partial and ordinary derivatives. Some equations of dynamics of liquidpropellant rocket engine do not contain time derivatives. The methodology of synthesis of optimal controls with the smallest value of the norm at each moment of time in systems with distributed and lumped parameters, some equations of which do not contain time derivatives, has been developed. The need for such control arises, for example, when determining the boost pressure in the hydraulic tanks of the hydraulic system; when determining the boost pressure of the fuel tank, which ensures stable operation of the heating furnace. The developed methodology can also be used to study stability of such systems. For example, when studying the stability of operation of a rotarytype wind turbine with a vertical axis of rotation together with a pump. The shaft that transmits the torque of the wind turbine to the pump has a considerable length, so the problem is solved, taking into account the elasticity of this shaft. 
Algazin S. D., Solovyov G. H. Formulation of the flutter problem of a plate of variable thickness of arbitrary shape in the plan. Trudy MAI, 2022, no 125 By the method of mathematical modeling the flutter of orthotropic plate of rectangular shape in plan at different angles of attacking stream is investigated. For numerical modeling of unstable oscillations of a plate the effective numerical algorithm without saturation which allows on a rare grid to receive admissible accuracy in the approached decision is offered. The type of eigenform depending on the angle of direction of the attacking flow velocity vector is studied numerically. The resulting quadratic eigenvalue problem can be reduced to a double sized standard linear eigenvalue problem. The term «panel flutter» refers to the flutter of a thin plate, shell, or membrane when typically, one of the surfaces is exposed to airflow and the other to still air. The panel then experiences elastic, inertial and aerodynamic forces, which can lead to dynamic instability of the structure. The paper shows that the resulting quadratic problem for eigenvalues can be reduced to a standard linear problem for eigenvalues of twice the size. Questions related to the existence, uniqueness and regularity of the solution are not considered in the work. We refer the interested reader to the work. The first recorded occurrence of flutter for circular cylindrical projectiles appears to have been on a German V2 rocket. The study of the stability of the oscillations of a thin plate of arbitrary thickness in the plan, which in the plane , occupies the region with the boundary and is blown by the gas flow, leads to a nonselfadjoint spectral problem for the amplitude value of the deflections , , which is obtained by generalizing the results of Kiyko I. A. and Ilyushin A. A. 
Levitskiy D. Y., Fedotenkov G. V. Nonstationary stressstrain state of the Timoshenko plate. Trudy MAI, 2022, no 125 Rapidly developing technical progress poses new, more complex and interesting tasks for engineers. This did not bypass the area of problems of the mechanics of a deformable solid body, and specifically the theory of plates. Plates and shells are extremely widely used in the construction of a wide variety of engineering structures. At present, nonstationary problems in the theory of plates remain poorly studied. In this work, vibrations of the Timoshenko plate under the action of nonstationary pressure are studied. investigated. The plate is assumed to be infinitely extended. To describe the movement of the plate, the wellknown equations of the S.P. Timoshenko. The solution method is based on the principle of superposition, according to which the normal displacements of the plate are a convolution of a given pressure with an influence function in spatial coordinates and time. The influence function for a plate is its formal displacements under the influence of a special type of pressure, namely, a unit concentrated force applied instantaneously in time. Mathematically, such a distribution is given by the product of the Dirac delta functions. A spatial problem is considered in a Cartesian rectangular coordinate system. In this case, expansions in double trigonometric Fourier series and the integral Laplace transform in time are used to construct the influence function. The original coefficients of the expansion series are determined analytically using the second expansion theorem for the Laplace transform. Using the principle of superposition and the constructed original of the influence function, the solution of the problem of nonstationary oscillations of a rectangular Timoshenko plate, as well as displacement at a point under the influence of a distributed load, is obtained. The paper investigates the response of the hinged Timoshenko plate to the impact of various nonstationary loads. For the solution, a numerical algorithm was developed and implemented on a computer. Examples of calculation of the deformed state of the plate are given. 
Snazin A. A., Shevchenko A. V., Panfilov E. B. Investigation of the finite element mesh local adaptation in the problem of supersonic flow near body. Trudy MAI, 2022, no 125 The traveling at supersonic speed generates a detached bow shock wave ahead of it. Downstream of that, the flow attains large increases of pressure and temperature, which are responsible for the high drag and aerodynamic heating. High drag values increase fuel usage and reduce the ratio of payload to total takeoff weight [1]. The paper considers supersonic flow at Mach number M=4.2. The condition of adhesion and isothermicity with a temperature T = 300 K is established on the streamlined surface of the object of study. The flow is considered axisymmetric with respect to the OX axis. The simulation was carried out in a twodimensional formulation on a structured prismatic grid containing 506 thousand elements, 65 elements account for the boundary layer. The ratio of the diameter of the main cylinder to the length of the needle is L/D = 1.4. During the calculation, the mesh cells are adapted in the zones of flow inhomogeneities. The number of adapted cells is 835 thousand, the number of unadapted cells of the original grid is 234 thousand. A homogeneous grid with the size of the cells corresponding to the adapted cells would contain about 2687 thousand cells. Thus, local adaptation allowed to reduce the amount of calculations by 2,5 times. As a result of the calculations carried out, the difference in the distribution of the pressure coefficient on the surface of the model and in the position of the head shock wave between the adapted and nonadapted grid is clearly traced. Comparison of the results of visualization of flow inhomogeneities in supersonic body flow obtained experimentally on a wind tunnel and numerical modeling. The results of numerical simulation are in good agreement with experimental data. The calculations presented in the article showed that the use of local grid adaptation in the areas of gasdynamic inhomogeneities allowed not only to reduce the cost of computing, but also to achieve a good agreement of numerical results with the results obtained experimentally on a supersonic wind tunnel. 
Sposobin A. V. Calculation of the large particle interaction with a supersonic shock layer using the meshless algorithm. Trudy MAI, 2022, no 125 The presented work deals with the numerical modeling of the twophase flows, namely, the computation of a blunt body supersonic flowaround by a viscous gas flow with an admixture of a small amount of large particles, which, after reflection from the surface, go outward the shock layer, being moved by the inertia towards the incoming flow. Testbench and numerical experiments reveal that the motion of high inertia particles changes the structure of the gas flow in the shock layer, and impact jets herewith directed to the body being formed cause the gas pressure increase near the surface areas and a multiple growth of the convective heat flow. A computational model of the blunt body supersonic viscous flowaround with an admixture of large solid particles was developed in threedimensional space. The system of nonstationary NavierStokes equations in conservative variables is being numerically solved by the meshless method, which employs the cloud of points in space of computational nodes for the gas flow parameters representation. The spatial partial derivatives of gasdynamic values and functions, containing them, are being approximated by the least square method on the set of nodes distributed in the area of computation. Nonviscous flows computing is being performed by the AUSMPW+ method in conjunction with the third order MUSCLreconstruction, while viscous flows are being computed by the secondorder scheme. Each particle, as well as a barrier streamlined by a flow, is being surrounded by a cloud of computational nodes belonging to its domain and moving together with the particle in space. The computational nodes position is being adapted to the body shape and allows resolving the flow in the boundary layer with enough accuracy to determine the convective heat flow from the gas surface. The gas state computing at the nodes associated with the particles is being performed by solving the NavierStokes system of equations in a moving coordinate system attached to the moving particle. A model of evolution of a single cloud of computational nodes is built. The nodes that fall into the domains overlapping zone are being temporarily excluded from the calculation, and external nodes of one domain become neighbors of the nodes of another domain to compute both viscous and convective fluxes between nodes with account for transformation of the gas state vectors between moving coordinate systems. Integration of the gasdynamic system of equations in both basic and local systems of coordinates is being performed by the explicit RungeKutta method. The proposed model was verified by comparing the gas flowaround of the stationary and moving particles while maintaining relative velocity of the incoming flow. The software implementation of the presented algorithms based on the OpenCL parallel heterogeneous computing technology with the possibility of simultaneous usage of several GPUs for the calculation of the same task was performed. The authors performed computations of the particles movement in the shock layer near the sphere surface flown around by the supersonic airflow with the Mach number of M = 6. The particle was being launched along the sphere axis of symmetry, as well as at an angle to it. Appearance of local zones of higher pressure and multiply strengthened heat flow on the sphere surface is being observed. Gasdynamic interaction of a pair of particles in the shock layer, which started one after the other with a time interval between them, was simulated. Having fallen into the supersonic wake region of the first particle, the second particle, moving under the action of aerodynamic drag force, moves away to a significantly smaller distance from the sphere surface than the first one. The built computational model and the software, developed on its basis, provide wide opportunities for the numerical study of the gasdynamic interaction of large particles with the shock layer. 
Belyaev B. V., Lebedev A. S. Methodology for predicting the residual resource during depressurization of aircraft. Trudy MAI, 2022, no 125 When determining the flight safety of aircraft, one of the urgent tasks is to diagnose a possible violation of the tightness of compartments during operation. Mechanical damage to sealed compartments of aircraft can occur due to fatigue, wear, thermal load, creep of the material, shock load, elastic deformation, surface fatigue, radiation damage, erosion wear and other causes. Leakproofness tests during the preparation of aircraft for operation are not always able to determine microcracks or other design defects that lead to a violation of the tightness of the device during flight. The article is devoted to the topical topic of diagnostics of the process of functioning of sealed compartments of aircraft with through microcracks. In the article, expressions are obtained that allow us to describe the patterns of changes in the leakage of the working medium through through cracks, depending on their changing geometry. An algorithm has been developed for constructing patterns of changes in the leakage of the working medium from sealed compartments in the presence of developing through cracks in their shells. Typical patterns of changes in the leakage of the working medium over time through through cracks are given. The results of calculating the time of depressurization of the compartment are presented, depending on the length of the through crack, the degree of its opening, as well as the free volume of the sealed compartment. The results presented in the article make it possible to more correctly diagnose failures of aircraft in flight operation. In addition, the results obtained make it possible to solve the inverse problem for instrument and habitable compartments of spacecraft. Namely, having the data of telemetric information about the parameters of the gas state (pressure and temperature) inside the compartment and the change of these parameters over time, it becomes possible to diagnose the characteristics of micron densities in the conditions of orbital flight. This, in turn, makes it possible to estimate the time reserve for localization of leaks or to make a decision for an emergency landing of a manned spacecraft. The proposed technique for diagnosing the tightness of aircraft during flight operation can be used to justify the requirements for sensors and pressure detectors in the hermetic compartments of aircraft and for the parameters of the system of reserve gas reserves. In case of emergency leaks during flight operation, it is possible, using the proposed methodology, to determine the remaining time reserve for eliminating the consequences of an accident, ensuring the safety of crew members or emergency landing on the Ground. 
Kolodezhnov V. N., Veretennikov A. S. Flow in a cylindrical channel of a nonlinear viscoplastic fluid. Trudy MAI, 2022, no 125 A combined rheological model has been proposed for viscoplastic working media that exhibit a nonmonotonic dependence of viscosity on shear rate. This model assumes three typical behaviors in three adjacent ranges of shear rate variation. In the first range, the dependence of the shear stress on the shear rate is described by a linear function and characterized by a constant viscosity value. In the second and third shear rate ranges, this dependence is approximated by nonlinear functions describing dilatant and pseudoplastic behavior. On the basis of such a model, the solution to the steady flow of fluid in a cylindrical channel has been obtained. It is shown that three different flow patterns can be implemented depending on the level of pressure drop along the channel length. For each of the schemes inside the channel, characteristic zones of flow should be identified. In the case of the most complex third flow pattern inside the channel, four zones with different mechanical behavior of the fluid should be distinguished. In such a situation, the zone of plastic flow is formed in the central part of the channel in the vicinity of its foreandaft axis of symmetry. The next zone is characterized by shear flow with a constant viscosity value. Two more zones of nonlinearviscous flow, in which the fluid exhibits dilatant and pseudoplastic behavior, are formed in the vicinity of the channel wall. Expressions for determining the boundaries of flow zones, and expressions for calculating the liquid velocity profile and the dependence of the volume flow on the pressure drop were obtained. The influence of the main parameters of the system under consideration on the velocity distribution characteristics and the dependence of the volumetric flow rate on the pressure drop over the channel length has been analyzed. 
Sha M. ., Sun Y. . Theoretical study of hydrogen degradation processes of drop impact erosion of structural materials. Trudy MAI, 2022, no 125 The unique physical and chemical properties of hydrogen and its practically unlimited resources on our planet in the composition of water make it possible to rely on hydrogen energy systems in the development of energy [1,2]. Industrial products, components and assemblies, structural elements, as a rule, operate in aggressive hydrogencontaining media (corrosive, erosive). Rain erosion damage, caused by repeated droplet impact on wind turbine blades, is a major cause for concern, even more so at offshore locations with larger blades and higher tip speeds. Hydrogen, penetrating into the metal of the product and being absorbed in it, changes the chemical composition, structure, and also redistributes the fields of internal stresses. These processes, generalized by the term «degradatio», prepare and stimulate the development of microdiscontinuities of various scales. At the moment, despite intensive research, hydrogen degradation is still an unsolved problem of metal physics, theoretical and practical materials science. It is known that the maximum destructive effect of hydrogen is observed when hydrogen has maximum diffusion mobility and activity, that is, at the stage of unsteady diffusion. Moreover, as the author notes, destruction under the influence of diffusionmobile hydrogen is little predictable and most dangerous due to the high diffusion mobility of hydrogen and the ability to redistribute under the influence of various physical fields, and there is also uncertainty about the magnitude of the critical concentration of hydrogen in the destruction zone. Since during the electrification of the working fluid, the surface of the working blades is exposed to electrophysical phenomena, conditions appear for increasing the absorption of hydrogen by metal, including in a diffusionmobile form. These conclusions about the significant impact on the damage to the blades of the flood are consistent with the conclusions. Based on the above qualitative assessments of the process of the impact of a stream of wet steam with charged droplets on the blade material, it is obvious that the magnitude of the negative effect on electrical processes depends mainly on the magnitude of the ion current in the space of the flow part. 
Averyanov I. O., Wasilchenko A. G. Mathematical model of air damper with permeable fabric shell. Trudy MAI, 2022, no 125 
Gerasimchuk V. V., Zhiryakov A. V., Kuznetsov D. A., Telepnev P. P. Computational and experimental method of accounting for the dewatering system in the analysis of natural frequencies and waveforms. Trudy MAI, 2022, no 125 The article is devoted to the issue of ensuring the adequacy of the developed finite element models of oscillators to real samples of the spacecraft. In the computational and experimental method, the correction of KE models of dynamic systems minimizes the difference in values between the target characteristics of the real design and the computational model. The main stages of the method are:
The computational and experimental method of accounting for the dewatering system in the analysis of natural frequencies and waveforms allows us to obtain an adjusted model fully suitable for further development of spacecraft control algorithms on a system (dynamic circuit) as close as possible to the real one. Using the example of two oscillators — a solar panel wing and a rod for carrying out scientific equipment — the article demonstrates practical and theoretical techniques for correcting finite element models using experimental research data. Based on the results of the fullscale determination of the natural frequencies and vibration patterns of the structure, the correction of finite element models developed using the Femap with NX Nastran package was carried out, and the adequacy assessment (verification of the correspondence of the model to the real system) of the dynamic circuit of the spacecraft, taking into account the influence of the dewatering system. The achieved difference between the target characteristics of the real design and the calculated model was less than 9%. 
Buzhin I. G., Antonova V. M., Mironov Y. B., Antonova V. A., Gaifutdinov E. A. Comparative analysis of the time delay of telecommunication equipment STP and SDN. Trudy MAI, 2022, no 125 The article considers the architecture of softwaredefined networks, their principle of operation, as well as the protocols for the interaction of the controller with network devices. The main components of traditional networks are investigated, including a comparative analysis of the time delays of telecommunications equipment of traditional and softwaredefined networks. There are 4 types of delay in modern data transmission networks: packet processing delay, packet delay in the queue, packet transmission delay along the line, propagation delay. The operation of the spanning tree algorithm is considered, its main advantages and disadvantages are highlighted. A comparative analysis of traditional and softwaredefined communication networks is carried out, the features of building corporate networks based on the SDN concept are considered. A network model was built in the Mininet emulator, in which an analytical assessment of the time delays of the SDN telecommunications equipment was carried out. As a result of the experiment and comparison of the obtained data, two different approaches to the network response to topology changes can be evaluated. The experiment showed that the traditional approach to building networks is vulnerable to changing the network topology, which introduces certain network delays and is the reason for the decrease in network performance. 
Kamensky K. V. Trajectory instabilities and onboard navigation system characteristics influence on synthetic aperture radar image quality. Trudy MAI, 2022, no 125 The goal of this work is to determine requirements imposed on onboard navigation system for the radar that is to be placed on a small unmanned aerial vehicle and to work in stripmap sidelooking synthetic aperture mode with linear frequency modulated continuous wave. To achieve this goal the methodology is proposed to investigate trajectory instabilities effects on radar image in continuous wave synthetic aperture radar. The same methodology can be used to obtain the estimates of onboard navigation system characteristics impact on radar image quality. These characteristics are: measurement accuracy of radar antenna system phase center coordinates and data sampling frequency. The proposed methodology is based upon the use of backprojection method to process a track signal obtained through direct simulation in the condition that there is only one point reflector on the illuminated scene. Quality of the amplitude radar image obtained this way can be estimated by objective criteria: main lobe width and side lobes relative level in the point reflector’s response. The results of the proposed methodology implementation are estimates used to choose the onboard navigation system for a specific radar. In this paper the cases were investigated where trajectory instabilities are absent, represent a constant value, a linear function, or a nonlinear function (sinusoid). It is concluded that onboard navigation system data sampling frequency should be not less than track signal sampling frequency in slow time, and acceptable accuracy of coordinate measurement depends on expected intensity of trajectory instabilities. The practical value of the conducted work is in that the proposed methodology allowed to provide rationale for requirements imposed on the onboard navigation system characteristics. 
Moroz A. V., Sahno I. V., Sherstuk A. V. Technology of image transmission in an ultrasonic communication line. Trudy MAI, 2022, no 125 The paper presents a description of a largescale physical modeling of a data transmission channel in the ultrasonic range through a medium, designed to solve the problems of evaluating testing of groundbased tests of an endtoend radar path of a spacecraft with a synthesized aperture antenna and groundbased equipment for digital processing and formation of radar images. As a subject of research, digital information packages are considered, formed from a color or monochrome image, sequentially transmitted through a distribution medium. The main elements of an ultrasonic data transmission system are similar to those used in radio data transmission channels. The need to solve this problem is due to the shortcomings of mathematical modeling in the form of introduced restrictions and assumptions. Thus, the aim of the work is to develop algorithms, software modules for transmitting raster (amplitude, analog) images and clarifying the research methodology on an ultrasonic data transmission system, as an integral part of the laboratory layout of the endtoend radar path of a spacecraft with a synthesized antenna aperture. The proposed largescale physical modeling is based on the principle of linebyline formed from a raster image of digital information packets that are sequentially transmitted in the ultrasonic range. After receiving and digital processing by a software receiver, the information is restored in the form of an image matrix. The result of the work is a developed laboratory setup in the form of an ultrasonic data transmission system, which makes it possible to obtain an assessment of the quality of transmitted information packets with bitmap images. The technique for studying the noise immunity of a digital ultrasonic data transmission line has been refined. Algorithms for digital signal processing and software for the ultrasonic data transmission system have been improved. The technical characteristics of the layout are experimentally determined and the limits of its change are specified. The values of the signaltonoise ratio are determined, at which there are no failures during the transmission of a raster image with a size of about bits. It is shown that the implemented model of the ultrasonic data transmission system can be used for image transmission when modeling the endtoend information path of earth remote sensing systems. The visibility of the simulation results makes it possible to use the ultrasonic data transmission system in the educational process when studying the principles of construction and operation of data transmission systems and methods of programmatic signal reception and processing. The next stage of the work will be the transfer of acoustic holograms obtained at the location acoustic complex, which will make it possible to form a hardwaresoftware stand for modeling the radar channel of a spacecraft with a synthesized antenna aperture. 
Anan’ev A. V., Ivannikov K. S., Filatov S. V. Construction basic principles of communication systems based on unmanned aerial vehicles. Trudy MAI, 2022, no 125 The research object in the article is air communication element: a communication system based on unmanned aerial vehicles, the relevance of which is justified in the previous works of the authors. However, despite the variety of related studies conducted, there are a fundamental questions number, without answering which it is impossible to understand the essence of creating a communication system based on unmanned aerial vehicles and determine its final purpose. So, on the one hand, unmanned aerial vehicles are an extremely important resource, in practice, which will always be in short supply. Therefore, talking about a fullfledged independent communication system based on unmanned aerial vehicles is very doubtful. On the other hand, there are very striking examples of the practical use of unmanned aerial vehicles as communications repeaters. It is only clear that the main condition for creating a communication system based on unmanned aerial vehicles is its organic inclusion in the overall communication system. Given the above, the subject of research article are the principles of creating a communication system based on unmanned aerial vehicles. Accordingly, the article purpose is to develop them based on a generalization of the existing backlog on known and promising technical and organizational and technical solutions in the field of communications. In the interests of developing the principles, first of all, the general scientific method was used, which consists in systematizing the existing knowledge, as well as the universal method — the method of analysis. The result of the work is a generalized list of principles for building a communication system based on unmanned aerial vehicles. A number of principles are formed in the development of the previously existing ones. At the same time, new principles are proposed: reasonable selfsufficiency, current interaction and evolutionary creation, etc. The developed principles can be used as the basis for practical work on building a communication system based on unmanned aerial vehicles and are the starting point for the formation of its technical appearance. 
Teplikova V. I., Sentsov A. A., Nenashev V. A., Polyakov V. B. Analysis of the direction pattern of a flat multielement active phased array. Trudy MAI, 2022, no 125 The article presents a study of a technique for correcting distortions in the radiation pattern parameters caused by the mutual effect of radiators, on the example of a rectangular active phased antenna array with the following number of radiators: 64 in the azimuthal plane, and 8 in the elevation plane. The authors considered the dependence of the main characteristics of the directional diagram on the beam deflection while electron scanning and the change in the strength of the electromagnetic field during the cosinesquare amplitude distribution forming on the pedestal. The nature of the dependencies is determined and a technique is proposed for controlling the distortions of the characteristics occurring while the beam deflection. This technique realization will allow correcting the directional pattern, having distortions due to the changes in mutual effect of radiators, obtaining the required characteristics of active phased antenna array, and implement operation modes, which require keeping the antenna array parameters unchanged. The following initial data is necessary when developing an algorithm: the number of rays, minimum scanning step, and the beam setting accuracy. As long as the result of this algorithm realization represents a data array, it is necessary to pay special attention account for the minimum memory size required for the initial data storage for the algorithm. This technique realization allows correcting parameters of the directional pattern, which contains distortions due to changes in the mutual effect of radiators, to obtain the required the APAA characteristics. Its application allows employing the radar operating modes, which require keeping the antenna array parameters unchanged. 
Kasmerchuk P. V., Vernigora L. V. Practical use of EPM and DE ephemeris. Trudy MAI, 2022, no 125 The design of interplanetary space missions is impossible without knowledge of the position of solar system objects and their dynamics. To determine the position and speed of an astronomical object at a specific point in time (on a specific date), special tables called ephemeris are used. Modern ephemerides are built on the basis of integrating rather complex equations of motion that take into account the gravitation of many bodies in the solar system, including large asteroids and transNeptunian objects, relativistic effects, perturbations from the dynamic compression of the Sun, mutual perturbations of the planets, the Sun and the Moon, etc. When building dynamic models ephemeris, data from radar observations of planets, laser observations of the Moon, data on the parameters of the movement of spacecraft during their approach to large planets, the results of interferometry with very long bases, etc. are used. To date, one of the most accurate are the Ephemeris of Planets and Moon (EPM) ephemerides developed by the Institute of Applied Astronomy of the Russian Academy of Sciences (IPA) and the Development Ephemeris (DE) ephemeris of the NASA Jet Propulsion Laboratory (JPL). Various variants of the DE series ephemeris appeared in the 60s of the XX century, the EPM ephemeris began to be created in 1974. The coordinate system used in a particular version of the ephemeris must be specified in the documentation. In most versions, the coordinates are as close as possible to the International Celestial Reference System (ICRS — International Celestial Reference System). The origin is the barycenter of the solar system. The X axis is directed to the vernal equinox at the J2000 epoch, the Z axis is perpendicular to the plane of the Earth’s equator, the Y axis completes the system to the right. The resulting coordinate system is independent of the Earth’s rotation. Units of measurement of coordinates are kilometers, measurements of time are days of barycentric coordinate time (TDB). The Julian day is used. Algorithms for converting a calendar date to a Julian day and vice versa can be found in. There are quite a few tools that allow you to calculate the ephemeris data of astronomical objects, for example, online ephemeris services, as well as offline libraries. However, if the task is to use ephemeris in your own software, in which for some reason the use of thirdparty libraries is impossible or there are high performance requirements for subroutines working with ephemeris, which require specific code optimizations, you can use the text representation of ephemeris in the DE format available for free download from the IPA and NASA servers. 
Kulvits A. V., Zhitnikov T. A., Mikheev O. Y. Theoretical aspects of the formation of a cluster of small spacecraft. Trudy MAI, 2022, no 125 The article discusses the theoretical aspects of the substantiation of the ballistic structure of the cluster of small satellites. For the ballistic justification of the small satellites cluster, it is necessary to solve several interrelated tasks. First, it is necessary to justify the parameters of the orbits, the functioning of which would allow the cluster to successfully solve the target task. Secondly, after launching the small satellites into orbit, it is necessary to provide the required configuration in space, which is determined by the ballistic structure. Thirdly, due to the influence of disturbing factors acting on the small satellites while moving in orbits, the configuration will collapse over time. Therefore, the stable relative position of the small satellites in the cluster can be provided by the justification of the ballistic structure in orbits of the same radius and inclination. For the three small satellites as part of the formation implementing the tasks of radio monitoring by the differencerangefinder method (DRM), acceptable performance indicators are achieved when the small satellites form an equilateral triangle during operation, since in this case the accuracy indicators of the DRM are optimal, while the onboard equipment also imposes restrictions on the formation in the form of minimum and maximum relative distances between satellites. Over time, the triangle formed by three small satellites deforms, while the indicators of solving the target problem decrease. Thus, the task is reduced to determining the set of parameters of the orbits of the small satellites cluster with a restriction on the relative position, which will ensure the maximum time functioning of three small satellites in the cluster of the required configuration. The proposed approach to solving this problem is based on the decomposition of the problem of finding optimal parameters into two special cases, which make it possible to determine the range of acceptable variants of ballistic structures of the small satellites cluster and thereby significantly reduce the area of possible iteration when solving the optimization problem. The analysis of the parameters of the small satellites orbits and the ballistic structures of the cluster makes it possible to ensure a stable relative position of the small satellites in space with the required periodicity. The results of solving the multiparametric problem of searching for a ballistic structure can be used at the stages of ballistic design of satellite systems consisting of clusters of small satellites. 
Tanygin M. O., Chesnokova A. A., Ahmad A. A. Increasing the speed of determining the source of messages by limiting the set of processed data blocks. Trudy MAI, 2022, no 125 The purpose of the study consists in developing a mathematical model, which allows evaluating the computational complexity of the original method of i the messages source identifying, which is based on forming the groups of messages and checking the condition of belonging to the target source for the entire group. An increase in reliability and decrease in computational complexity in the method under study is being achieved by assuming that the sequence of messages from the source to the receiver is maintained. This allows cutting down the number of messages involved in the group forming, and, accordingly, reduces the number of options for such groups’ formation. To study the computational complexity of the algorithm for the groups of messages forming, the number of elementary operations for comparing hashes of such messages was studied, i.e. of the basic operation determining membership of a particular message to the structured set being formed. The length of the message hash, the number of interacting subjects of the distributed system, a number of messages in the group, as well as the parameter limiting the set of messages being analyzed, were the parameters of the model. The process of messages receipt to the receiver was represented as a linear dynamic process characterized in each discrete time instant by the probabilities of a certain number of messages receipt from the target source and all other sources of the distributed system. The results obtained with this model allow asserting that the condition of warranty of the messages sequence, received by the device, does not change complexity of the message source detection. It stays linearly dependent on the length of the group of messages and a number of devices interacting in the framework of the system of devices. At the same time, in absolute numbers, the number of comparison operations is reduced by two orders of magnitude compared to the group forming method, which does not employ the stationary property of information flows between the distributed system components. 
Kuznetsova S. V. Features of crossplatform mobile applications development using Xamarin. Trudy MAI, 2022, no 125 Today, the development of mobile applications is one of the most actively developing sectors of the IT industry. In this regard, there are many projects for the development of applications on mobile platforms. Digital transformation in the aviation industry covers the production of aircraft, as well as passenger and cargo transportation. As for transportation, the work of airlines, airports, interaction with passengers, customers of cargo transportation, the functioning of a unified air traffic management system deserves special attention. One of the technological trends actively developing today in terms of digitalization of the aviation industry is the development of mobile applications for aviation, including aircraft construction, air transportation and airport services. Mobile applications provide significantly faster access to data and are an effective means of interaction regardless of the user’s location. For example, they provide quick access to technical information and direct data entry, optimizing engineering and production processes. The classic version of mobile application development is native development, in which a separate application is developed for each operating system (OS), which is quite expensive and time—consuming. An alternative is a crossplatform technology, the main purpose of which is to provide developers with a tool for parallel creation of applications for multiple operating systems at the same time. This will allow them to write a single source code for several mobile platforms, but the result of each individual build will be separate executable files. Obviously, crossplatform development is needed to optimize the cost and speed of development, as well as application support. At the same time, the output result is no less qualitative than with native development. Currently, there are the following most popular crossplatform frameworks: Xamarin, React Native, Flutter, and NativeScript. They are very different and not in all situations will be equally useful (or even necessary in principle). The article discusses the technology of developing crossplatform mobile applications Xamarin: the principles of developing crossplatform mobile applications using it are outlined, the main features provided to developers within this approach, its advantages and disadvantages are presented. A range of issues related to the design, implementation and testing of mobile applications is considered: the use of the MVVM architectural pattern, the XAML markup language to describe the user interface, a possible development environment. A methodology for creating crossplatform mobile applications on the Xamarin platform is presented, containing a brief, consistent and comprehensive description of all stages of development. 
Brekhov O. M., Ratnikov M. O. Comparative analysis of test systems for FPGAS and their environment. Trudy MAI, 2022, no 125 This work is devoted to the study and analysis of currently used FPGA test systems and their system environment, developed by both domestic and foreign researchers. More than 30 test systems based on the use of: builtin selftest structures (BIST), specially designed systems and systems that partially or completely use the target firmware are considered. The systems in question were used to solve various tasks: FPGA input control, testing of internal interconnection resources, testing of individual cells and embedded IP cores, testing of the FPGA system environment (external connections of FPGAs and the power subsystem), analysis of electrical, dynamic and functional characteristics in various conditions, search for single failures and failures. The systems used in the study of microcircuits for resistance to laser exposure, the flow of charged particles (including studies within the Alice CERN project and studies conducted by both FPGA suppliers and thirdparty researchers to compare the characteristics of various FPGAs), the accumulated dose of radiation, elevated temperature and changes in supply voltage are considered. The systems and methods that are used to debug the FPGAbased system are also considered. Also in the list of test systems considered there are systems used as a demonstrator of the application of methods for analyzing energy consumption, dynamic characteristics, reliability and fault tolerance, as well as testing and developing systems based on FPGAs. The result of the work is a classification of the considered systems, an analysis of the advantages and disadvantages of the considered systems and proposals for the further development of FPGA test systems and their system environment. 
Dorozhko I. V., Gorokhov G. M., Kirillov I. A. Methodological approach to the development of a decision support system for the operator of an automated process control system based on dynamic bayesian networks. Trudy MAI, 2022, no 125 The article describes a scientific and methodological approach that can be used in the development of intelligent decision support systems for operators of automated process control systems. The proposed approach is based on the mathematical apparatus of dynamic Bayesian networks, as well as the basic concepts and relations of the theory of reliability and technical diagnostics of systems. The initial data are information about the algorithm of the system functioning and the course of the technological process, information about the reliability (structural and logical circuits, failure rates of elements) of technological equipment, as well as diagnostic models linking the types of technical conditions and diagnostic signs. It is proposed to use temporal connections (temporal logicalprobabilistic dependencies) in a dynamic Bayesian network to simulate changes in the technical states of elements of technological equipment and describe the dynamics of the technological process. A posteriori conclusion allows combining heterogeneous initial information and incoming new data to obtain a comprehensive assessment of the progress of the technological process and the condition of technological equipment in order for the operator to make an informed decision on the continuation or suspension of the technological process, search for the causes of abnormal situations and the choice of proactive measures. The implementation of this approach is given on the example of a decision support system for an operator of an automated control system for technological equipment of a booster refueling system, the peculiarity of which, when analyzing reliability, is the need to take into account elements with three incompatible states — operable, failure of the «break» type and failure of the «closure» type, affecting the course of the technological process in different ways. The variants of using the developed decision support system for the current control of the technological process, forecasting and retrospective analysis in the search for the causes of abnormal situations are shown. 
Minakov E. P., Privalov A. E., Bugaichenko P. Y. A model for evaluating the control efficiency of multisatellite orbital systems. Trudy MAI, 2022, no 125 The article is devoted to solving the important problem of evaluating the control efficiency of multisatellite orbital systems. The article introduces definitions of an orbital system (OS), a multisatellite OS (MS), and an control system of OS. The relevance of the problem of evaluating the control efficiency of MS by stochastic modeling is substantiated. Based on the principle of A.N.Kolmogorov, the MS control efficiency indicator has been identified and its mathematical model has been developed. The mathematical formulation of the problem of evaluating the control efficiency of MS, which consists in determining the efficiency coefficient of management, expressing the degree of achieving optimal efficiency at the current values of the controlled parameters, is realised. A model for evaluating the efficiency of MS management in the form of a continuous Markov chain has been developed. With the application of the developed model, the evaluation of the control efficiency of a perspective MS of remote sensing the Earth based on the Berkut spacecrafts, which is being developed within the framework of the Sphere program, has been carried out. The dependences of the control efficiency on the quality indicators of the control system for solving various remote sensing tasks has been obtained. The developed model can be used at the stage of development of methods, techniques and algorithms of MS control for their elaboration, verification, calibration, optimization, evaluation of the impact of their quality indicators on the control efficiency of MS, and also for justification of requirements for them and confirmation of compliance with the declared requirements. 
Ezrokhi Y. A., Kizeev I. S. Assignment of the compressor performances at mathematical modelling of the aviation gas turbine engine. Trudy MAI, 2022, no 125 Efficiency of aviation engine mathematical model (EMM) application at various stages of the engine creation substantially depends on accuracy and «physical» descriptions of working procedure in airgas channels of the engine and its units. As now the course of creation of the aviation gas turbine engine (GTE) and the aircraft works can depend on reliability of the engine parameters and performances estimation, increase of EMM accuracy is rather important problem. One of the most significant components of the gas turbine engine mathematical model accuracy is accuracy of the basic engine units’ performances; in particular, elements of the compression group (fans and compressors). In article features of the assignment of compressor performance with air extraction from its airgas channel in gas turbine engine mathematical model are considered. It is shown that the distributed air extraction can lead to appreciable compressor performances exfoliation, especially to its part located behind a place of extraction; it is necessary to consider at the aviation gas turbine engine parameters computation. For this purpose the relative extracted air flow, and also part of the compressor work from enter to an air extraction place are defined. These parameters allow calculating the physical air flow, enthalpy and temperature of extracted air. As show results of the numerous experimentcalculated researches, now widely used simplified technique of air compressor extracted air enthalpy definition can lead to considerable errors in GTE parameters calculation. The main reason of wrong calculation aviation GTE parameters is discrepancy of methodical approaches to independent estimated and/or experimental definition of units’ performance to how this performance is used in engine mathematical model. That correctly to use the performance of engine units (for example, compressor cascades) in integrated engine mathematical model, it is necessary to know, how they were characterization and that is understood as value of this or that experimentally received parameters have been received. Techniques of the compressors’ cascades tests results handling for its characterization, calculation of the air extractions’ parameters, and also the turbine power for a drive of the considered compressors’ cascade in core and gas turbine engine system are presented. 
Fedorova L. A., Sofin A. P., Gorshkov L. K., Uhanov I. G. Assessment of stability of the root link of the manipulator under the action of axial load on it. Trudy MAI, 2022, no 124 The development of space manipulation systems is directly related with obvious expansion of the possible range of work and operations that can be carried out in difficult and dangerous conditions with technical orbital objects and equipment installed on them. By now, the main construction option used has developed — a hingetype manipulation system of different degrees of complexity. Modern manipulators must be carried out with condition of maintaining stability of elements. Taking into account the priority of influence of the root link on stability of the manipulator as a whole, it is proposed to investigate the equilibrium positions of the rod for stability at a range of deviations π < φ < π. Criterion of stability of equilibrium position for systems with holonomic and stationary constraints located in conservative force field is determined by LagrangeDirichlet theorem: According to the theorem equilibrium positions of a conservative system in which its potential energy has minimum are stable. The results of the study of stability by taking into account angle of inclination of the link are determined by the dependence between the angle of inclination φ and the dimensionless force λ. The formation of the real appearance of a service multilink manipulator for use in space conditions should be carried out on the basis of taking into account functional tasks and the available database on specifics of creation and use of existing devices. The studies carried out to date indicate that, along with geometric interpretation, which provides an assessment of the initial structure and approximate dimensions of the manipulator elements, it is necessary to analyze the operational loads that determine stability of circuit elements. Obviously, the actual dimensions of the manipulators will be determined by motion parameters (for example, angle of rotation) of hinge elements. The calculations performed show that to a large extent the condition and, consequently, the operability of the root link are determined by the axial load. The proposed studies allow us to assess the danger of such a load and give recommendations on the design of the manipulator, taking into account the properties of the elastic hinge and the size of the links. This will prevent monotonous departure from the considered equilibrium positions or fluctuations increasing in scope over time. 
Popov I. P. Absolute reference systems in relative motion. Trudy MAI, 2022, no 124 It was noted that the problem of reference system selection at relative motion of the objects of commensurable mass is of particular relevance while interplanetary flights at a considerable distance from the planets. For the same inert objects moving relative to each other, different coordinate systems give completely different total kinetic energies of objects. In this sense, it impossible to recognize them as equivalent. It is obvious that none of these coordinate systems can be considered as absolute. Only the system which selection completely eliminates arbitrariness, can be considered as the absolute system of cordinates. This requirement is met by a system in which the total kinetic energy of objects is minimal. The absolute coordinate system coincides with the center of mass of the objects and with the epicenter of their hypothetical repulsion from the state (hypothetical as well) of mutual immobility. After a hypothetical repulsion, the velocities of objects relative to the center of mass acquire the same values as in the absolute coordinate system. Along with a wide variety of reference systems at the mutual motion of unaccelerated objects, including those associated with these objects (these reference systems can be considered relative), there is one absolute reference system associated with the center of mass of the objects under consideration. The considered repulsions of objects are calculated and may have nothing to do with reality. The number of objects while the absolute coordinate system definition is not limited by anything. It may be both two objects and a star system. 
Smirnov A. S., Smolnikov B. A. Construction and analysis of rational modes of rigid body motion control. Trudy MAI, 2022, no 124 The paper considers the motion of a rigid body under the action of a control moment, formation of which is carried out in various ways and meets the specific control goals. The main properties of the collinear control and its modified version are discussed, which lead to an increase or decrease in both kinetic energy and kinetic momentum, and as a result they allow overclocking or braking of a rigid body. Orthogonal control is also considered, which does not violate the constancy of kinetic energy and kinetic momentum and leads to a reorientation of the rigid body in space. In addition, combined control options are constructed, which have the features of both collinear and orthogonal controls in their structure. First control option allows dissipating or accumulating kinetic energy at a constant kinetic moment, and the second option, on the contrary, leads to a decrease or increase in the kinetic moment at a constant kinetic energy. Such controls can be interpreted as rational, since they are efficient, have a fairly simple structure, and are convenient for practical implementation. Moreover, physical analogies are given for the constructed control options, which make it possible to correlate their action with inertia forces, dissipative forces of external and internal friction, as well as gyroscopic forces. Based on various methods, exact analytical solutions are constructed for the mentioned modes, and these solutions describe the process of controlled motion of a rigid body and demonstrate its properties. The results obtained in the work are not only of fundamental theoretical significance, but can also be used in solving applied problems of rigid body dynamics. 
Barkova M. E. Safety system for shredding space debris in orbital conditions. Trudy MAI, 2022, no 124 The space debris shredding safety system is a fundamental system in the processing of space debris into fuel directly in orbit. This study is devoted to the possibility of testing the technology for processing metallized debris on Earth, as well as the development of the concept of a safety system for shredding space debris. In the wreckage of the stages of rockets, propellant vapors remain, which, if crushed, can provoke an explosion. The main problem of the article is the development of the concept of a safety system for shredding space debris directly in orbit. The purpose of this work is to consider ground tests of the technology for processing metallized space debris into fuel. The relevance of this work lies in the concept of a safety system for shredding space debris directly in orbit. The most important source of nonfragmentation debris was more than 2,460 firings of solid rocket motors, which released aluminum oxide (Al_{2}O_{3}) in the form of micrometer dust and slag particles ranging in size from mm to cm. The main cause of inorbit explosions is due to residual fuel that remains in tanks or fuel lines, or other leftover energy sources that remain on board after a rocket or satellite stage has been dropped into Earth orbit. These fragmentation events are thought to have generated a population of objects larger than 1 cm, numbering on the order of 900,000. The sporadic flux from natural meteoroids can only dominate the flux from humanmade objects near sizes of 0.11 mm. 
Rabinsky L. N., Babaitsev A. V., Shesterkin P. S. Investigation of the effect of rolled products in layers of aluminumfiberglass on static and dynamic properties. Trudy MAI, 2022, no 124 The composite materials is a new invention of the material combination which can be used in the aircraft industry. The main purpose of the invention is to have the lightweight structure and anticorrosion effect with better strength. This type of materials is hybrid because of the combination of the metal and fiberglass. The new characteristic of this hybrid material is a combination of each advantage of aluminum, steel and fiberglass. Based on previous studies, the manufacturing of aluminumfiberglass based material must follow the concept of interlaminar for the better bonding. This work is devoted to the study of the effect of rolled products in aluminum layers of aluminaglassreinforced plastic. In particular, the study of static and dynamic properties along and across rolled products was carried out. Aluminum alloys are the most common materials used in the aviation and space industry. These alloys have a relatively high specific strength and a lower density than steels. Consistent optimization of the design of aircraft elements in terms of reducing their weight and the simultaneous fulfillment of specified strength requirements has led to the emergence of metalpolymer composite materials. These materials have a number of advantages over aluminum alloys: lighter weight, higher specific strength, crack resistance. Aluminum fiberglass plastics developed in Russia in the Russianlanguage literature are called SIAL. Over the past few years, a large number of works have been devoted to the study of materials of this type including in relation to the modeling of large parts of aircraft structural elements. This material consists of alternating layers of aluminum alloys and fiberglass reinforced epoxy. A composite of this type is a promising, improved material with improved specific strength, damage resistance, impact resistance, and fatigue strength. Formed from several layers of aluminum alloy sheet and layers of glassfiberreinforced glassfiberreinforcedpolymer (GFRP), aluminoglassreinforced plastic behaves like an elasticplastic material primarily due to the presence of layers of aluminum alloys, and its complex failure mechanisms are determined by its composite structure. 
Medvedskiy A. L., Martirosov M. I., Khomchenko A. V. Fracture and deformation mechanics of polymer composites in the presence of multiple bundles of arbitrary shape under the action of dynamic loads. Trudy MAI, 2022, no 124 Currently, elements of structures made of polymer composite materials (PCM) are becoming increasingly important, which have a number of advantages: high specific stiffness and strength, low specific gravity, high wear resistance and fatigue resistance, as well as the ability to create unique mechanical properties depending on the requirements for the finished product, etc. With the above advantages, PCM products also have disadvantages, which include their sensitivity to damage. To prove that the strength characteristics of PCM structures meet the certification requirements, it is necessary to carry out computational, theoretical and experimental work according to methods that allow us to show that the designed structural elements from PCM fully meet the requirements. Such elements can be largesized aggregates (wing and tail panels, center section panels, forkill, wing spars, stabilizer and keel), or they can be quite compact (fairings, fairing, nacelles, structural elements of mechanization). Traditional structural metal materials, due to their stable characteristics, the duration of the period of preservation of mechanical and technological properties, provide the specified strength characteristics of the aviation structure. The level of safety provided by the PCM construction should not be lower than the level of safety provided by the metal construction. In the work, studies were carried out to assess the impact of internal defects (damages) of the type of bundles of various sizes and locations in layered elements of structures made of polymer composite materials (PCM): a cylindrical reinforced shell, a reinforced cylindrical panel, a rectangular reinforced plate. A technique is proposed for modeling structural elements made of PCM with defects of the type of bundles under the action of dynamic loads of various nature. 
Kanashin I. V., Grigorieva F. L., Khromov A. I., Grigoriev Y. Y. Tension of a strip made of a compressible material with a continuous velocity field under plane deformation. Trudy MAI, 2022, no 124 The subject of the study of the presented article consists in determining conditions of the moment of a crack nucleation at the stretching of the plane sample from the compressible material under conditions of the plane deformation. The purpose of this study is studying the process of stretching a flat sample made from compressible material with a continuous displacement velocities field under the plain strain conditions. The material compressibility associated with the mass conservation law, which is formulated in the form of the equation of continuity, leads to a density change while loading process, in accordance with which the logarithm of the material derivative of density in time is being added to the system of equations defining the displacement velocity field. This system is being converted to a system of inhomogeneous wave equations. The following methods were applied while this research conducting. They are: — Analytical method for the velocity and deformations field determining; — Averaging method for obtaining the mean value of the auxiliary function on the sphere; — Method of descent for transition from the sphere surface integration to the circle integration. In the course of the studies, an intermediate result, namely the general solution of the system of wave equations for the velocities field determining, was obtained. The results of the study can be applied while mathematical models developing of the behavior of real structures’ elements in the problems of modern mechanical engineering and construction, as well as in assessing their strength. 
Cherkasova M. V. Approaches to modeling the process of erosion products deposition on the gas discharge chamber walls of an ion engine. Trudy MAI, 2022, no 124 Currently, many tasks of space exploration use ion engines, including highfrequency ion thrusters. At the same time, special attention is paid to the terms of active engine operation. In the design of a ion thruster, the ion beam is extracted from the discharge plasma and accelerated using an electrode system operating on the principle of electrostatic lenses. The accelerating electrode of such system is subject to erosion due to bombardment with exchange ions. Electrode damage results in engine performance change for two reasons. Changing the electrode configuration worsens the characteristics of the ion beam and also the sprayed electrode material penetrates the discharge chamber and settles on its walls, changing the discharge characteristics. Extensive theoretical and experimental studies have been devoted to the erosion of the accelerating electrode itself, while the problem of deposition of sprayed material on the walls of the gas discharge chamber has not been practically investigated. This paper proposes a physical and mathematical model for depositing sputtered atoms of accelerating electrode material on the walls of a gas discharge chamber of a highfrequency ion engine. Twodimensional model of spatial sputtering of accelerating electrode surface by exchange ions and interaction of sputtered material atoms with primary beam ions is considered. Possible ranges of emission angles of sprayed atoms penetrating inside the discharge chamber through the holes of the emission electrode are estimated. Based on the created model, calculation of the accelerating electrode erosion of the twoelectrode ionoptical system with the accelerating electrode from molybdenum was carried out. In the first approximation, the penetration of sprayed molybdenum atoms into the plasma of the discharge chamber was simulated. An estimate of the distribution of polluting atoms over the conditional model surface was obtained. Quantitative estimates of surface contamination rate have been made. The developed physical and mathematical model of processes will allow in the future to create an engineering methodology for calculating the dynamics of deposition of sprayed material on the walls of the gas discharge chamber of a highfrequency ion engine. The use of such a technique will reduce the time of life tests and better predict the change in engine performance for long service life. 
Pismarov A. V., Kirpichev V. A., Sazanov V. P. Prediction of the resistance of tired threaded parts. Trudy MAI, 2022, no 124 A method for threaded parts surface hardening is being widely employed to the fatigue strength increase. Maximal result of its application is being achieved under conditions stresses concentration with regard for the fact that destruction occurs as a rule in the places of prismatic shape violation. Thus, establishing a qualitative and quantitative relationship between static stresses and fatigue resistance of threaded parts is highly uptodate task. A large group of parts in assemblies and structures has stress concentrators in the form of threads. Threaded joints are highly loaded elements, which operation defines the strength and reliability of the structure as a whole. The strength of threaded parts operating under conditions of an asymmetric cycle, which average stresses are stipulated by the tightening force, depends mainly on the tensile working stresses, as well as on the strengthening treatment. In this regard, development of the technique for determining the endurance limit of the threaded part by the known residual stress diagrams as well as average stresses of the cycle using the linear elastic fracture mechanics provisions presents interest. Based on the foregoing, the object of the study in this work is highcycle fatigue, and the subject of study is threaded parts with residual stresses. The purpose of the study consists in developing a technique for predicting the fatigue resistance of the threaded parts by developing a technique for assessing the relationship between the stress intensity factor (SIF) and highcycle fatigue characteristics. Using the graphs of the distribution of residual stresses in the cavities of threaded parts as the initial data, the nature of the SIF dependence on maximum stresses of the cycle of a hardened threaded part was determined in the work. The graph can be presented in the form of the three sections. The first section corresponds to the state when the crack edges are completely pressed against each other, that is, the fatigue crack does not open, despite the presence of cycle tensile stresses. The second section corresponds to the state when the crack opens from the inside, while the sides of the crack remain closed. The third section represents a straight line running parallel to the similar dependence of the nonhardened thread and corresponds to the scheme when the crack is fully opened. The starting point of the third section of the graph corresponds to the maximum stress. It was found from the calculations that the criterion for the most optimal technological mode of thread manufacturing with creation herewith of a compressive residual stresses field is the stress of the transition point of the second section into the straight third section. Starting from this point, the fatigue crack opens completely. The proposed technique for predicting the fatigue resistance of threaded parts from the standpoint of linear fracture mechanics allows predicting maximum amplitude of the cycle. 
Sanchugov V. I., Rekadze P. D. Calculation of hydrodynamic characteristics for bench systems. Trudy MAI, 2022, no 124 The problem of article is the developing the V.P. Shorin’s load variation method for solving the problem of determining the own dynamic characteristics of a hydraulic pump as a vibrations source of the working medium. The method consists in calculating the pumps dynamic characteristics (considered by models of equivalent oscillation sources) while changing the bench systems behind the pump, registering pressure pulsations and converting into the own pump characteristics by V.P. Shorin’s models of equivalent oscillation sources. In known works, dynamic models of bench systems, as a rule, are idealized, either do not take into account all the elements of bench systems, or implement a limited set of bench systems (such as «acoustically open end», «acoustically closed end», etc.). While calculating the dynamic characteristics of bench systems, we propose to use information about the design and geometric dimensions of the systems flow part. The article summarizes the main aspects of calculating the bench systems dynamic characteristics, their hydrodynamic schemes describing the influence of both cavities, throttles and main lines, and connecting fittings, adapters and the units’ internal channels are presented. The work aims to create special bench systems with known dynamic characteristics in order to solve the problem of determining the own dynamic characteristics of a hydraulic pump. The developed models of bench systems with a throttle, a cavity, a «short» and an extended pipeline at the pump outlet, when used in the load variation method, will make it possible to calculate the pulsating state of the working medium behind the hydraulic pump both in the hydraulic systems of machine tools and in the fuel systems of a gas turbine engine at the early stages of design. The results of the work can be important for engineers and designers of hydraulic systems, because they contain specific formulas and recommendations on how to use them. 
Petrov I. I., Serdyuk D. O., Skopincev P. D. Fundamental solutions for orthotropic cylindrical shell. Trudy MAI, 2022, no 124
A circular cylindrical shell of constant thickness is considered, the side surface of which is affected by nonstationary load. The shell material has symmetry with respect to the median surface, is linearly elastic, orthotropic. The motion is described in a cylindrical coordinate system associated with the axis of the cylindrical shell. The mathematical model of the object under consideration is described using the Kirchhoff — Love hypotheses. Fundamental solutions (Green’s functions, influence functions) are constructed for a cylindrical shell of great length, as well as a cylindrical shell pivotally supported at the ends. The Green function for an orthotropic shell is a solution to the problem of the effect of an instantaneous concentrated load on the shell, modeled by the Dirac delta function. To find the influence function in the case of an unlimited cylindrical shell, expansions into exponential Fourier series in angular coordinate, the integral Laplace transform in time and the integral Fourier transform in longitudinal coordinate are used. The inverse integral Laplace transform is being performed analytically, and the original integral Fourier transform is being found using numerical methods for integrating rapidly oscillating functions. In the case of a limited cylindrical shell, expansion into double trigonometric Fourier series in the angular and longitudinal coordinates is applied, as well as the integral Laplace transform in time. The inverse integral Laplace transform in this case is performed analytically. Verification of fundamental solutions has been carried out. Examples of calculations are given. The results are presented in the form of graphs. A new numericalanalytical fundamental solution of the dynamic problem of elasticity theory for an orthotropic elastic thin unlimited cylindrical shell is obtained, as well as an analytical fundamental solution in the case of a limited KirchhoffLove shell. The convergence of the solution is established. To demonstrate the realism of the constructed functions, examples of calculations for one variant of the symmetry of an elastic medium are presented. The nature of the movement of nonstationary perturbations allowed us to evaluate solutions. Fundamental solutions open up opportunities for solving new contact and inverse problems of load identification, allow performing applied research on calculating the stress and strain levels of orthotropic shells. 
Averyanov I. O., Zinin A. V. Mathematical model of nondeformed cargo landing system with dampers to rigid plane landing process. Trudy MAI, 2022, no 124 To calculate dependability measures for developed dropped cargo landing systems with dampers we usually use statistics from similar models and mathematical statistical modelling of landing process. In this article we describe the mathematical model of dynamics landing process for cargo dropped systems with dampers we developed for its further using in statistical modelling. This mathematical model considers all the phases of dynamic landing process — from the phase when air dampers start resisting to the phase of system stopping — and is able to indicate typical failures like excessive acceleration and system overturn. It should also be appropriate from time cost point of view. Analysis of sources shows that existing models are not appropriate for the considered task: almost all of them consider only the dampers resisting phase; in case of finiteelement models solutions it is not appropriate according to the time cost. A rigid body with dampers dropped to the rigid landing area (plane) is consided. The body is freely located in 3D space in the beginning of the process as well as the plane. We use dynamic equations of forces and moments equilibrium in 3D space with reactions from dampers and the plane. The body and the plane interaction realizes with contact algorithm. To solve the equations numerical simulation with finitedifference schemes is used. There are two tasks presented to demonstrate how the developed model works. The first task considers the translational motion of the dropped body with dampers. The second one — complex body movement. As the considered equation system is closed the algorithm we developed has benefits related to the existing solutions from the point of view of time cost. Thus, the dynamic landing model we developed is appropriate for statistical modelling tasks. 
Zvonarev V. V., Vitaly V. ., Popov A. S. Method of calculating influence of frequency scanning interference on reliability of signal reception with QPSK modulation. Trudy MAI, 2022, no 124 To accurately assess the channel resource and determine the maximum signal attenuation in a complex electromagnetic environment, the article describes a technique that allows calculating the probabilistictemporal characteristics of a radio channel with high accuracy and reliable forecasting. As the main characteristics of a radio channel in a complex electromagnetic environment, the article considers the probabilities of bit and character errors affecting the reliability of signal reception. The article presents a mathematically correct method for calculating the probabilities of symbolic and bit errors of coherent optimal characterbycharacter reception of a radio signal with QPSK modulation in the presence of interference with linear frequency modulation inside the symbol. The basis of the technique is the representation of a fourdimensional probability measure of the vector of output voltages of the correlation channels of the receiving device in the space of the eigenvectors of the covariance matrix of this vector. The results of the article are necessary to calculate the influence of interference in a connected radio channel, when finding the probabilities of symbolic and bit errors. The calculation method is integrated into the energy calculation algorithm of the transmission channel in the presence of interference with LFM modulation. The developed technique of the influence of frequencyscanning interference on the reliability of receiving a signal with QPSK modulation makes it possible to accurately determine the probability of symbolic and bit errors at given values of the level and deviation of the interference frequency. The results obtained show that the curves of the average probabilities of symbolic and bit errors have a threshold character. The presence of interference with linear frequency modulation significantly degrades the quality of the communication channel, completely disrupting the reception of information at the values of the interference level when the interference level exceeds the signal level. The extension of the graphs to the region of zero signal value at zero and nonzero interference value shows that the average probability of a symbolic error is 0.75. In the same case, the probability of a bit error is 0.5. It is determined that the phaseaveraged interference probabilities of correct reception, and, consequently, errors in receiving signal positions in the presence of interference with LFM modulation, are the same, which allows the calculation of the transmission channel to be limited to using as an average the probability of receiving one signal position. 
Letfullin I. R. Standards and technologies of shortrange wireless communication networks. Trudy MAI, 2022, no 124 The article discusses the main technologies and standards for wireless data transmission, provides an overview and comparative analysis of shortrange wireless technologies («last 100 meters» technology), and also discloses some technical characteristics. The advantages and disadvantages are shown. For the analysis of nearradius technologies, a method for comparing parameters was chosen based on information from domestic and foreign literature, scientific articles and publications. The analysis contributes to the selection of the most optimal wireless data transmission standard for organizing an efficient nearrange network aimed at solving the main problem of Internet of Things devices — ensuring the secure connection of a large number of devices with limited power deployed over a wide area and meeting the performance criteria of the Internet of Things. Currently, shortrange wireless communication is based mainly on Bluetooth, UWB, ZigBee and WiFi standards, which are based on IEEE 802.15.1, 802.15.3, 802.15.4 and 802.11a/b/g/ah standards, respectively. The specified IEEE standards define physical (PHY) and MAC levels for wireless communication in a range of about 10100 meters. Based on the review, it can be concluded that 802.11ah is the most promising nextgeneration WiFi technology for largescale applications of the Internet of Things with low power consumption, which combines support for high data transfer rates over long distances, low power consumption, low latency, and thanks to builtin mechanisms such as RAW, TWT and TIM, significantly reduces collisions when accessing the channel, and also provides the required QoS. It is also important to note that wireless technologies are changing rapidly following the needs of the Internet of Things market and it is recommended to monitor updates to existing standards and technologies, as well as the emergence of new shortrange technologies. The requirements for power consumption of devices, data transmission security, high network fault tolerance, the ability of devices to withstand radio interference and ease of connection remain unchanged. 
Ageev F. I., Voznuk V. V. A method for calculating the probability of a bit error of optimal characterbycharacter coherent reception of binary opposite phasemanipulated signals in the presence of narrowband noise interference in the radio communication channel. Trudy MAI, 2022, no 124 The article is solving the problem of the bit error probability computing of the optimal characterbycharacter coherent reception of the opposite phasemanipulated signals (BPSK signals) at the presence of the inadvertent narrowband noise interference. The article considers the Gaussian noise interference with uniform spectrum limited by the frequency band and arbitrary power, entering the pass band of the BPSK signals receiver. Application of the receiver based on either correlator or matched filter tuned to the signal being considered under conditions of the intrinsic noise of the receiver presence only is being understood to in the article as the optimal receiving of the opposite phasemanipulated signals (BPSK signals). Analytical expressions were derived and a technique for computing the bit error probability of the optimal characterbycharacter coherent receiving of BPSK signals with the presence of both intrinsic receiver noises and narrow band noise interference. The wellknown expressions, being used for the probability estimation of the bit errors of the optimal characterbycharacter coherent reception of the BPSK signals against the background of the white Gaussian noise, form the basis of the obtained relationships. Based on the obtained results, the basic inferences were formulated ,and asymptotic probability estimations of the bit error of the optimal coherent BPSK signals reception at the presence of both intrinsic noise of the receiver and narrow band noise interference for the uttermost narrow band and wide band Gaussian interference were obtained. The article demonstrates the presence of the narrow bane noise interference, which spectrum overlaps the BPSK signal spectrum leads to the noise immunity degradation of the information radiotransmission channel, and the degree of the noise immunity degradation herewith depends drastically on both power, spectrum width and this interference place of location in the BPSK signal spectrum. 
Moiseev S. N. Simulation of the difference error in target tracking by airborne radar and optoelectronic stations. Trudy MAI, 2022, no 124 The article deals with the task of modeling differential errors of target tracking by the onboard radar and optoelectronic stations of navigation and weaponaiming complexes of aircraft in the interests of studying their accuracy characteristics. The presented work employs simulation model, developed for obtaining statistical estimation of the onboard highprecision target tracking systems based on employing wellknown noise characteristics of reference measuring means and tracking channels of target tracking systems under study. The article demonstrates that the misalignment between the aircraft radar and optoelectronic stations leads to the shift occurrence in the differential error of the target tracking. The law of the shift in the differential error changing of the target tracking is similar to the misalignment error changing. This may be used for the error value evaluation and its program minimization. 
Ermakov P. G., Gogolev A. A. Software complex of algorithms for autonomous determination of the angular orientation parameters of unmanned aerial vehicles. Trudy MAI, 2022, no 124 The article «Software complex of algorithms for autonomous determination of the angular orientation parameters of unmanned aerial vehicles» by P.G.Ermakov and A.A.Gogolev compares three approaches used for an Attitude and Heading Reference System (AHRS), namely Mahony, Madgwick and Complementary filters. For attitude determination on UAV’s board widely used a magnetic and inertial measurement unit (MIMU). MIMU consists of a 3axis MEMS gyroscope, accelerometer and magnetometer. The accelerometer measures the acceleration of a UAV, the gyrosocope measures the angular rate of a moving object, and the magnetometer measures the Earth’s magnetic field. So, Mahony uses a proportional and integral controller to correct the gyroscope bias, Madgwick uses the gradientdescent algorithm. Both approaches use a quaternion representation, which a fourdimensional complex number representing the orientation of an object. A Complementary filter is proposed that combines accelerometer output for low frequency attitude estimation with integrated gyroscope output for high frequency estimation. Madgwick obtains better heading orientation than Mahony and Complementary AHRS approach in respect of the root mean square error (RMSE) of the Euler angles when compared to the motion capture system. 
Abadeev E. M., Piskunova O. I., Tretyakov A. V. Method for adaptive control of the longitudinal movement of a smallsized aircraft with a signal limitation of the integral component. Trudy MAI, 2022, no 124 The article conducts the studies of characteristics of the promising control and longitudinal motion stabilization system of a dynamic object, such as a smallsized aircraft (SSA), based on the technique of the adaptive signal formation [1, 2]. The study of the control method being considered was conducted by the mathematical modeling method of an isolated pitch channel with implementation of the proposed SSA control laws at rather characteristic external impacts on it. Simulation was being performed under conditions of changes by the given “slow motions” law [3] of the flight parameters such as altitude and velocity. Comparison of the control processes of the SSA with the system being proposed and control processes with the conventional proportionaldifferential control technique [4] adapted to the given situation in [5, 6, 7] was performed to evaluate the effectiveness of the newly introduced control specifics. The relevance of the presented work consists in the fact that the velocity increase being achieved by the proposed technique, overshoot degree reduction and, correspondingly, increasing the control signals processing accuracy may contribute to the SSA maneuvering and controllability characteristics improvement. 
Rozin P. E., Simonov A. V., Gordienko E. S., Zaiko Y. K. Inflight calibration of the "DEKART" CubeSat magnetometer. Trudy MAI, 2022, no 124 As part of the ADCS of CubeSat LEO satellites magnetic control systems have become the most widespread. The magnetic control system, as a rule, magnetorquers that create control momentum and magnetometers. Magnetometers are used in this system to determine the direction and magnitude of the Earth’s magnetic field intensity vector. To reduce the cost of creating a CubeSat spacecraft, it is common practice to use household digital magnetometers. These devices are characterized by low accuracy due to the lack of calibration of the zero offset and mutual orthogonality of the measurement axes of the device. Thus, the task of developing an algorithm and software implementing it for calibration of magnetometers become very important. The algorithm considered in the paper is based on the processing of measurements of a 3axis magnetometer on Earth, after their transmission from the spacecraft. The processing consists in searching by the method of configurations minimum of the functional, as a result of which the values of the calibration parameters are determined. The value of the functional is determined as a result of numerical simulation of the spacecraft flight and determination of the calculated value of the Earth’s magnetic induction vector, followed by comparison with the transformed measured induction vector of the Earth’s field. The practical application of the algorithm is considered on the example of the «DEKART» spacecraft launched as part of the UniverSat program on September 28, 2020 at 14:20 (Moscow time) from the Plesetsk cosmodrome. «DEKART» CubeSat spacecraft was developed and assembled at the D.V. Skobeltsyn Research Institute of Nuclear Physics of Moscow State University. 
Piyakov A. V., Sukhachev K. I., Dorofeev A. S., Bandyaev V. A. Electrodynamic accelerator control system with calculation of motion parameters in real time. Trudy MAI, 2022, no 124 The work relates to the field of accelerator technology and is devoted to improving the control system of an electrodynamic linear accelerator of dusty charged particles. The existing accelerator is used to simulate the factors of the space environment and makes it possible to study the effect of highspeed micronsized particles on the elements of the surface of the spacecraft under conditions close to real. However, this accelerator has a complex control system that requires the operator to control a large number of parameters in real time and to constantly adjust during the experiment. The need to measure physical quantities and calculate particle parameters, as well as manual control, increase the error in the formation of accelerating pulses in the dynamic section, which leads to inefficient particle acceleration or the loss of most of them. The article proposes a new method for controlling a dynamic accelerator, the basis of which is a method for determining the parameters of a particle, which makes it possible to refuse any measurements other than timeofflight, made in an improved measuring section. The structure of the measurement section is presented in the article, while it is clear that minor changes are required in the already existing design of the accelerator. A control system has been developed that allows, according to data from timeofflight sensors, to automatically control the dynamic section of the accelerator with high accuracy. This is achieved, among other things, by refusing to use memory banks with precalculated voltage switching times on the drift tubes. In the new control system, the calculation of the particle position and its instantaneous velocity occurs in real time, since the calculation of the particle's specific charge is no longer required. Knowing the position of the particle in the path allows timely switching of the voltage on the drift tubes while the particle is inside them. The proposed method for determining the particle parameters and the control system have a calculation error associated with the discreteness of the measured time intervals. An analysis of the error and its influence on the acceleration process was carried out, from which it is clear that the system allows particles to be accelerated in a wide range of specific charges, and the maximum deviation of the particle coordinate when switching the voltage on the drift tubes does not cause it to leave the fieldless space of the drift tube. In addition, the system has a margin of accuracy, since the simulation was carried out for the existing accelerator design and an increase in the frequency of timeofflight sensors and a computer is not required, although this is possible if necessary. Thus, the proposed method for controlling a dynamic accelerator makes it possible to automate the process of conducting experiments and increase the efficiency of particle acceleration in an extended range of charges, masses, and initial velocities, and also makes it possible to increase the number of accelerating sections, thereby increasing the equivalent accelerating voltage of the system. 
Storozhev S. A. Multiagent control of the combustion chamber oxidizer using neurofuzzy technology in the MISO system. Trudy MAI, 2022, no 124 The an aircraft gas turbine engine (GTE) of aircraft from the point of view of control theory is a complex nonlinear object, the frame mathematical description of which is known a priori, has one input and several outputs. When operating a gas turbine engine, continuous monitoring of parameters is required (gas temperature behind the combustion chamber, rotor speed of the lowpressure compressor (free turbine), rotor speed of the highpressure turbocharger (gas generator). The selective controller controls these parameters, realizing control in different modes of operation of the gas turbine engine. Further The development of GTE control can be associated with the use of neurofuzzy control of the oxidizer flow into the GTE combustion chamber. Purpose: improving the control of the combustion process in the combustion chamber of the gas turbine engine. Methods: a new approach to designing an adaptive state controller based on neurofuzzy technology using triangular terms with equal bases equal to the interval 0–1, whose vertices are shifted according to the arithmetic mean of the path traveled by the input variables, is proposed. Determination of the degree of membership is performed by singletons, synchronously shifting depending on the change in input parameters using proportions. On the basis of the proposed approach to designing an adaptive state controller with an oxidizer flow, the relationship between the input parameters of the combustion chamber and the development of the control control with maximum speed is estimated using the area ratio method or the weighted average method. The idea of the experiment, using the designed state controller, is to estimate the temperature change behind the combustion chamber, which should not leave the specified zone. Results: the developed adaptive state controller is characterized by the best values of the probability of nonfailure operation during the experiment. Practical relevance: the research results can be used in the control of the combustion chamber. This can significantly reduce the uncertainty in the operation of the combustion chamber, ensuring a minimum release of harmful substances and guaranteed thrust of the aircraft. 
Sudarenko D. A., Kakadei M. S., Yazykov A. A. Compare of technology ADO.NET and SQLite for the development of LTCC structuralparametric description database. Trudy MAI, 2022, no 124 The technology of lowtemperature cofired ceramics (LTCC) is considered. This technology provides an inexpensive solution in the mass production of electronic devices in the field of telecommunications, medicine, automotive technology, military equipment, aerospace and other industries. In the process of implementing LTCC technology, difficulties were identified associated with the influence of a large number of parameters depending on the components used, the time of use and configuration of equipment at each stage of production on the quality of products. The parameters of technological operations (TO) are highlighted, grouping is made according to the characteristics of parameters: resource, process, result, control and management. In real life, there is no system that would collect all of the above parameters together, compare them and give recommendations for improving quality. In this paper, a method for creating, describing and modeling parameters in the form of information support based on a structural parametric description (SPO) according to regulatory documentation is proposed to improve the quality of production of microwave components. Based on this classification, workplace models are built, and the data is aggregated into the MS Access database management System (DBMS). Since Access has a number of disadvantages and is not, in fact, a fullfledged database, technologies were considered as a DBMS ADO.NET from Microsoft (the Sharp C language framework) and the Qt SQLite framework (in C++). ADO.NET manages both internal data (created in computer memory and used inside the application), and external, located outside the application — for example, in a database or text files. The Qt framework contains a universal interface for working with various databases. Databases in the Qt view are drivers for the QtSql module. By default, when installing the framework, the SQLite database is available, for the rest of the databases, installation and assembly of drivers for Qt is required. A comparative analysis of these databases has been carried out, on the basis of which it can be assumed that the SQLite DBMS is suitable for prototyping at the initial stage and crossplatform applications, and the DBMS ADO.NET it is more complex, but more promising in terms of commercial use. 
Zaitseva N. I., Pogarskaia T. A. Development of software complex for analysis and optimization of the aircraft assembly process. Trudy MAI, 2022, no 124 The presented work is devoted to describing the multiprocessor software complex ASRP (Assembly Simulation of Riveting Process), being developed as part of a joint project of Peter the Great St. Petersburg Polytechnic University and the AIRBUS SAS. This complex is meant for simulating and optimizing the aircraft assembly process, with account for the fact that aircraft building places rather strict requirements to the parts assembly quality due to high operational loads. The authors propose employing in the complex mathematical modeling and numerical optimization methods, which allow predicting and optimizing the quality of the parts joints prior to implementation of the technologies for the assembly line being developed. In the aircraft building industry, one and the same assembly technology is being employed while series assembly for all aircraft of the same type being assembled. Accordingly, while modeling the assembly process it is necessary to account for random assembly deviations, such as deviations of parts from the rated shape or errors in positioning. The ASRP suggests accounting for these deviations through modelling the random initial gap between parts. To optimize assembly processes, it is necessary creation and analysis of various options of the fixing elements positioning is required. A fundamentally new approach has been developed for the ASRP to optimize the temporary fastener patterns, based on the preliminary assessment of the stressstrain state of the assembled structure. When modeling assembly processes considering assembly variations and the fastener patterns optimizing, the necessity to solving many similar problems with hundreds of different initial data arises. For this reason, the ASRP suggests employing parallel computations for analyzing and optimizing the assembly processes. This presented article describes the structure of the ASRP software package, the developed methods for the assembly process modeling, methods for the initial gap modeling, as well as methods for optimizing the fastener elements placing. The efficiency of the proposed optimization methods and parallelization algorithms is being studied on a practical example associated with the analysis of the assembling process of the tail section of Airbus A350. 
Morozov A. Y. Interpolation approach in problems of modeling dynamic systems with ellipsoid parameter estimations. Trudy MAI, 2022, no 124 
Dementiev A. N., Klyuev D. S., Novikov A. N., Mezhnov A. S., Peterskova Y. A., Zakharova E. V., Dementiev L. A. Development of a method for spacetime processing of broadband signals in an adaptive antenna array. Trudy MAI, 2022, no 124 Numerous scientific articles and monographs are devoted to the theory of spacetime signal processing in antenna arrays. This type of processing is possible only in directional antennas, namely in adaptive antenna arrays, since they have a multichannel structure and allow you to identify the direction of signal arrival due to the accumulation of phase delay. Adaptive antenna arrays make it possible to form «nulls» of the radiation pattern in the direction of the interference signal by adjusting the vector of weight coefficients in the processing channels. The level of development of science interprets that these channels operate at the same frequency, that is, they are harmonic, which does not allow solving the problem of processing broadband signals. In this regard, a number of nuances arise that require more detailed theoretical and practical studies. At present, the issues of processing broadband signals in adaptive antenna arrays have not been studied both theoretically and practically. There is no clear understanding of the methods for selecting and calculating the vector of weighting coefficients in the frequency band. Also, the issue of receiving signals and suppressing interference, the sources of which are in motion, was not considered. These issues are relevant, since the development of modern technologies dictates the need to expand the spectrum of the transmitted signal, which makes it possible to increase the volume of transmitted information, ensure electromagnetic compatibility in conditions of saturation of the frequency range, and also increase the resolution. The article developed a method that allows spatiotemporal processing of broadband signals with the suppression of interference of various spectra, the sources of which are in motion. This method is based on the gradient descent method, which makes it possible to form «nulls» of the antenna array radiation pattern in real time and provide the required signal/(interference+noise) ratio at the output of the antenna array, which in turn provides the required bit error probability for transmission systems. Data and accuracy of determining the parameters of the object of observation and location for radar and radio navigation systems. 
Zhukov N. A., Kiselev I. A. Investigation of the influence of cutting tool flank face contact forces on the dynamics of end milling. Trudy MAI, 2022, no 123 In the modern machinery 5 axis end milling operations are widely used in the production of thinwalled workpieces with complex 3D surface geometry [13]. Such processes are always accompanied by vibrations of different elements of the technological system (e.g., workpiece, tool): free, forced, parametric vibrations may arise, as well as selfoscillations. One of the most undesirable vibration types are regenerative selfoscillations, which may cause dynamic instability of the steadystate cutting process: these vibrations arise due to the fact, that each tooth of the mill is cutting the surface, formed by a previous tooth, so the time delay effect is introduced [46]. At the early investigations of cutting dynamics it was observed, that vibrations amplitudes of the technological system’s elements decreased while machining with low spindle speeds [7,8]. This effect was called “process damping” and its presence was explained by contact interaction between the flank face of the tool and the machined surface [9]. The intensity of process damping is the higher, the lower is the ration of the mill’s teeth pass frequency to the vibrations frequency [10].
Modern timedomain models of 5 axis end milling processes lack process damping accountment [1719], so numerically simulated machining dynamics at low spindle speeds (comparatively to the arising vibrations frequencies) are not correct, which is extremely actual for machining of thinwalled workpieces from nickel and titan alloys. In this work a new timedomain numerical model of end milling dynamics of flexible workpieces is presented. This model allows to consider complex 3D contact forces between the workpiece and both rake and flank faces of the cutting tool during end milling dynamics simulation. Model’s structure and its main blocks are described. The developed model was used to perform numerical experiment on the influence of contact forces, arising on the flank face of the cutting tool, on the dynamics of the flexible workpiece end milling. Obtained numerical results qualitatively match well known experimental data from literature. 
Popov I. P. Artificial moment of inertia. Trudy MAI, 2022, no 123 The article demonstrates that creation of the “artificial mass”, which associates with neither volume, nor the density of the material, encased in the inertial object, is based on the requirement to the Newton’s second law satisfaction. As far as the equivalence principle of inertial and gravitational mass is not extended to the artificial mass, a device with the artificial mass may be incommensurably lighter than its mechanical analog with the same moment of inertia. This quality makes this device particularly attractive for application in aviation and astronautics, including light flywheels. The purpose of the study consists in analytical synthesizing of the artificial moment of inertia and identifying parameters determining it.
The existence of analogies between physical quantities of different physical nature does not automatically lead to the possibility of obtaining the corresponding functional dependencies. For this, technical means ensuring dimensionalities concordance of the dual quantities are necessary in the first place. If an artificial flywheel is being placed in a “black box”, it will be impossible to determine by any experiments whether an artificial or “natural” flywheel is inside it.
The main advantages of the artificial flywheel over a “natural” one are its incomparably lower weight and the possibility of electrically controlling the moment of inertia over a wide range by changing the magnetic field (excitation) and capacitance, which creates a good prospect for its application in automatic control systems. 
Korovaytseva E. A. Comparative study of soft shells of canonical meridian forms static deforming at inflation. Trudy MAI, 2022, no 123 The presented work compares behavior of the soft shells of revolution with various canonical shapes of meridian (semisphere, cylinder, torus, cone) from the nonHookian material at large deformations under the impact of the pressure uniformly distributed along the meridian. The shells’ sizes are being selected from the condition of the geometric sizes equity in the in terms of nondeformed shells surfaces areas.
The shells deforming is being described by the unified system of equations, applicable for any meridian construction form considered at arbitrary displacements and strains. Boundary conditions are being considered equal as well. Resulting relations of the nonlinear problem, being considered physically and geometrically, are formulated in the vectormatrix form. The problem is solved using parameter differentiation method algorithm. The initial nonlinear equation system herewith is being differentiated with respect to solution continuation parameter, which leads to interconnected quasilinear boundary and nonlinear initial problems forming. These problems are solved in steps using iteration method.
A number of features of the considered problem solution is established. In particular, for the hemispherical shell, the solution can be considered verifiable only until reaching some minimal value of pressure in supercritical area. However, from the calculations viewpoint, this problem solution possesses the highest iteration convergence rate. An ability of bearing the smallest magnitude of pressure among all the considered variants of shell meridian is characteristic for the conical shell.
For subcritical area, increasing of meridian and decreasing of circumferential strains is characteristic while approaching the fixed boundary of the shell, and for cylindrical shell, it is more intensive. Meridian and circumferential stresses in cylindrical shell exceed the ones in the spherical shell on the largest part of the meridian. In the toroid shell, stresses as well as strains remain minimal.
In supercritical area, the meridian strains in cylindrical and spherical shells decrease while the fixed boundary approaching. Strains in cylindrical shell become the smallest ones, and meridian strains in the toroid shell are the largest. Similar behavior is being observed for the stresses distribution along the meridian. 
Seregin S. V., Dobryshkin A. Y., Sysoev E. O., Zhuravleva E. V. The influence of the reinforcement of carbon thinwalled open cylindrical shells on free vibrations. Trudy MAI, 2022, no 123 Thinwalled cylindrical shells found wide application in various industries. The development of technology puts forward more and more serious requirements for the strength and stability of structures along with their low weight and cost. Such requirements are being applied to aeronautical engineering and unmanned aerial vehicles. The optimal solution in many cases consists in applying thinwalled shells made of carbon materials with high strength properties. The shell structures are being exposed to temperature and wind loads, variable atmospheric pressure during the aircraft flight and many other dynamic impacts. Thus, the structural materials of the shells should be lightweight and durable. Recently, carbon materials, which are an order of magnitude lighter and stronger that metal, are being applied more often. Under operating conditions, shells are being exposed to high dynamic stresses that may lead to adverse effects. However, the problem of the multilayer carbon shells dynamics is not fully understood up to now. Thus, for example, the known theoretical studies in a number of cases, have significant discrepancies in the values of the lowest frequencies of the vibration spectrum of reinforced shells with numerical calculations performed by the finite element method. This fact requires an experimental study on the behavior of low frequencies. The article provides an experimental study of the effect of multilayer reinforcement of thinwalled carbon fiber open cylindrical shells on their free vibrations. Experimental samples were created on the KomsomolskonAmur State University basis for the experimental study of the effect of multilayer reinforcement of carbon thinwalled open cylindrical shells on their free vibrations. Models of shells with singlelayer reinforcement were made of 2/2 12K1000600carbon fabric. Twolayer reinforcement was created from a layer of 2/2 12K1000200carbon fabric and a layer of 2/2 12K1000400 fabric. A threelayer reinforcement was created from three layers of 2/2 12K1000200carbon fabric. The experimental data was compared with the analytical solution. The experiments revealed an increase in the vibration frequencies of carbon thinwalled open cylindrical shells with an increase in the number of layers of carbon fabric reinforcement in relation to the values of frequencies obtained analytically. 
Zotov A. A. An analytical form for presenting a filler for threelayer systems, consisting of staggered coneshaped elements. Trudy MAI, 2022, no 123 This paper considers the problem of analytical determination for the stiffness characteristics due to the use of a filler in the form of a regular coneshaped (or pyramidal) cell’s system arranged in a checkerboard pattern for threelayer plates
At the moment, the most widespread are honeycomb, corrugated or folded fillers. The main filler’s advantages are low weight and high rigidity. However, there are circumstances that prevent their wider use. The closed volume formed by the core’s cells e promotes the accumulation of condensate, at the same time preventing its removal. On the other hand, there are technological difficulties associated with the provision and control of a reliable connection between a filler and bearing layers (especially on curved surfaces), thereby increasing the product cost. The structure of the cellular filler considered in the article largely allows to solve the above problems.
Due to the complexity and laboriousness of solving strength and stability problems for systems of variable stiffness, analytical solutions for a wide class of such structures are practically absent or hardly applicable in solving problems related to the design of products.
The article proposes a method for analytical filler’s representation in the form of a regular discrete coneshaped cell’s system, with the aim of further determining the geometric properties.
Based on the analysis of the filler’s shape under study, contemplation its shape as a surface described by the trigonometric Fourier series was proposed. However, upon further analysis of the problem, it was possible to reduce the function describing the filler’s geometry to a simpler form. The final version of the shape function was a set of coefficient, cosine and sine. Filler’s representation in the form of a similar function allows one to determine the variable bending stiffness of a threelayer package when solving the problems of bending of plates with variable stiffness.
Representation of the shape of the considered filler in this form with high accuracy conveys the true geometry of the product and allows to analytically describe the geometric stiffness characteristics of the structure (areas, moments of inertia and static section moments) included in the differential equations of bending and buckling of a variable stiffness plate. 
Mikhailova E. Y., Fedotenkov G. V. Transient deformation of the halfspacemembrane system. Trudy MAI, 2022, no 123 
Egorov I. A. Taking into account the features of the flow around the arcshaped wings at the design stage. Trudy MAI, 2022, no 123 Currently, arcshaped wings are widely used for smallsized missiles. Therefore, techniques are needed to determine the aerodynamic characteristics of such wings, primarily the lift coefficient.
1.The peculiarity of the arcshaped wing flow is reduced to three aspects
Reduction of local angles of attack
2. Reduction of the «useful» component of the local lifting force of the panel
3.The convergence of the wing panels, and the amplification of the mutual influence of the panels.
Consideration of all these aspects is possible when using the discrete vortex method.
The wing is divided into panels with a given pitch in span and chord. In each panel there is a Πshaped vortex.
When determining the geometric parameters that determine the position of the wing point relative to the vortex, it is necessary to take into account the curvature of the wing.
Two schemes of arcshaped wings are considered: with an opening angle of 90° and with an opening angle of 135°.
The scheme with an opening angle of 90° is taken as the basis for consideration.
The transition to a scheme with an arbitrary opening angle is reduced to a simple recalculation of coordinates.
The calculation is performed in the following sequence:
1.The coordinates of the wing points in space are calculated.
2.The parameters of discrete vortices in space are determined.
3.A matrix of coefficients of the system of equations is formed.
4.The angles of attack are determined taking into account the spatial orientation of the wing element
5.The circulation values and the value of the wing lift coefficient are determined.
The calculation results for a rectangular wing are presented.
The wing is divided into 24 panels.
Mach number M = 0.8, angle of attack α = 1º.
The conclusion:
1.The discrete vortex method is very convenient for constructing an arcshaped wing calculation model.
2.Acceptable calculation accuracy can be obtained already with a large grid.
3.The greatest influence on the accuracy of the calculation has an increase in the density of the grid along the span
4.To obtain acceptable accuracy, the curvature of the arched wing must be taken into account at all stages of the calculation
5.An arched wing with an opening angle of 135° has bearing characteristics close to those of a flat wing 
Kornev S. V., Pimenov I. A. Numerical investigation of velocity field behind the wing by different vertical position horizontal tail. Trudy MAI, 2022, no 123 The flow field of two lifting surfaces modeling wing and horizontal tail is investigated in this article. Aerodynamic characteristics and simulation of lifting surfaces’s flow pattern were calculated in the angles of attack were varied from 0 to 25 when the horizontal tail had have diverse positions in height: upper, initial and lower. As can be seen, if the horizontal tail has the lower location, it will be more efficient because the horizontal tail is located outside from vortex wake’s area behind the wing in high the angles of attack.
The main objective of this research is aerodynamic design’s optimization consisting in the choosing of horizontal tail position in height in order to reduce control system requirements and improving its reliability by reducing moment’s characteristics nonlinearity. Aerodynamic computation of lifting surfaces which geometry are the same surfaces of prototype MIGAT was calculated for determination an efficient horizontal tale’s position in height. Fluid flow and gas calculation with turbulence was done on base numerical solution total system of hydrodynamics’s partial differential equationscontinuty equation, NavierStokes equations, energy equation which were modified with Reynolds’s averaging procedure. The flow field around two lifting surfaces was computed in the software package Ansys Fluent. Visual simulation’ s analysis of velocity distribution has shown that the horizontal tail which has low and high position is located outside of wing’s vortex wave area in higher angles of attack. However, if an angle of attack increases, the horizontal tail which has higher location will be situated in wing’s vortex wave, that the lower horizontal tail. In this case, it will lead to pitch moment’s characteristics degradation. To sum up, when the horizontal tail has the lower location, it is more efficient because in this case, this variant has favorable characteristics of pitch moment, in spite of, lifting properties’s neverthless minor reducing compared with more high position of the horizontal tail. 
Khatuntseva O. N. Generalized analytical solution of the plane Poiseuille problem for the turbulent regime of incompressible fluid flow. Trudy MAI, 2022, no 123 The possibility of describing both laminar and turbulent modes of fluid flow based on the same equations has been investigated. It is proposed to consider the NavierStokes equations (NSE) in a phase space expanded by the introduction of an additional stochastic variable. As a result, an additional term appears in the expression for the total time derivative, characterized by the production of entropy due to the excitation of stochastic perturbations.
For laminar flow modes, entropy production takes zero value, the additional term disappears, and the transition to the NSE in their standard form is carried out, while the corresponding solutions describe only laminar flow modes.
The inclusion of an additional term, characterized by entropy production (which is always nonnegative), into the equations allows us to take into account the time irreversibility of physical processes in cases where this production is nonzero.
It is shown that the occurrence and maintenance of nondeterministic – stochastic processes – in a liquid is possible in those systems, where incompatible boundary condition occurs. In this case, the existence of one smooth solution becomes impossible, and we can only talk about the presence of two or more nonintersecting or nonsmoothly intersecting asymptotes of the solution. The region located between these asymptotes (or in the vicinity of the point of “discontinuity” of derivatives) is an uncertainty domain that generates a stochastic process.
As generalized solutions to problems with two asymptotes of the solution, functions were considered that are the sum of two terms, each of which is the product of two functions: one of which determines one of the asymptotes of the solution, and the second determines the degree of influence of this asymptote on the overall solution at each point of the studied domain.
The “laminar” and generalized “turbulent” solutions of the plane Poiseuille problem are found in this formulation. The comparison of the found solution with experimental data of the wallmounted universal velocity profile is given for different values of the Reynolds number. 
Gavrilova A. Y., Kulizade M. E., Cherkasova M. V. Plasmomechanical interpretation of excited inert gas atoms states. Trudy MAI, 2022, no 123 A plasmamechanical approach to the problems of gas kinetics has been developed to improve passive optical diagnostic methods. The article considers the solution of quasistationary system of equations of radiationcollision model of inert gases lowtemperature plasma depending on priority of electronic and photoprocesses. The system of linear differential equations of kinetics is being reduced to a matrix form with a nonzero right part, which is being interpreted as an influence factor, for which a relaxation matrix is being introduced. The obtained matrix equation is being solved by iterative methods for the selected final configuration of the inert gas atom levels (argon, xenon, krypton) using various models of influence factors.
If electronic processes are considered as an influence factor, then the calculated dependencies of electron concentration on the total number of nuclei correspond to the state of local thermodynamic equilibrium. Graphically, this dependence on a logarithmic scale is represented by straight lines. The populations of excited levels correspond to the Boltzmann distribution.
If photoprocesses are being regarded as an influence factor, then, a deviation from the rectilinear dependence of the electron concentration on the total number of nuclei is being observed in the area of low and high electron concentrations. However, the populations of excited levels still correspond to the Boltzmann distribution.
The dissociative recombination processes addition to the “influence factor” in the case of twotemperature plasma, when the electron temperature is much higher than the temperature of heavy particles, fundamentally changes the character of the diagrams. The article presents diagrams of the metastable states of heavy inert gases, which include a nontraditional hysteresis region. Without accounting for the dissociative recombination, the curves of the metastable state diagram degenerate into a typical dependence.
The metaequilibrium states diagram is useful for estimates in plasma spectroscopy, as well as for optical diagnostics of plasma flows. 
Gidaspov V. Y., Duong M. D. The effect of the properties of a real gas on solution of riemann problem in detonating gas. Trudy MAI, 2022, no 123 The article considers a selfsimilar Riemann problem on the border between multicomponent gases which properties are being described by a virial thermal equation of state with a singlefluid mixing model. A physicalandmathematical model, computational algorithms and numerical simulation results are presented. The computational model is implemented for the three cases, namely, the first one is “frozen”, i.e. physicochemical processes in gases do not originate, and the components concentrations do not change. The second one is “equilibrium”, which means that concentrations of chemical components satisfy the chemical equilibrium conditions. The third is a combined one, i.e. the of components concentrations to the left and right of the gap can be eother “frozen” or “equilibrium”. The solution of Riemann problem always includes a discontinuity separating the initial gas mixtures and, depending on the initial parameters, a fan of rarefaction waves or a shock wave propagating to the left and right of the discontinuity. In the case of an explosive mixture, a recompressed detonation wave or a ChapmanJouget detonation wave with a fan of rarefaction waves docked to it can propagate through it, while it is assumed that the composition of the combustion products is equilibrium.
A computational algorithm has been developed for solving the corresponding system of differentialalgebraic equations expressing the laws of conservation of mass, momentum and energy for the cases of continuous flows (fan of rarefaction waves) and discontinuous flows (shock and detonation waves), supplemented by thermal and caloric equations of state and, if necessary, thermodynamic equilibrium conditions.
Computational and theoretical studies of the decay of the gap at the boundary: argon – methaneair combustible mixture and helium – hydrogenair combustible mixture have been performed. The initial data ranges at which the results of calculations using the thermal equation of state of real and perfect gases differ significantly are determined. 
Privalov A. E. Unified software platform for develop of multiagent models of orbital spacecrafts constellation. Trudy MAI, 2022, no 123 The article proposes a unified software platform designated for multiagent models developing of orbital spacecraft constellation with various target purpose. Mathematical model of the software platform was developed at a high abstraction level, ensuring a generalized description of orbital spacecraft constellation operation, regardless its target purpose and life cycle stage. Besides, the basic systems of coordinates, employed in the spacecraft ballistics, as well as function of transition between them were defined in the space of the model functioning. These specifics allow considering this mathematical model as a basis for the multiagent models of the orbital spacecraft constellations of various target purposes. The objectoriented model based on the mathematical model in the form classes diagram, ensuring the platform program realization, was developed in the UML language
The software platform has realized in the Python programming language in the form of two packages, containing a set of classes and methods for developing multiagent models of orbital spacecraft constellation with certain target purpose. Besides the program platform, such model should include the following modules: user classes library, which are the platform subsidiary classes, reflecting the target purpose of the spacecraft constellation; the experiment control subsystem, and information analysis and display subsystem.
The unified software platform may be implemented as a core for the multiagent models developing of orbital spacecraft constellations with various target purposes. A high abstraction level allows creating models with various degrees of detail, corresponding to the life cycle stage of the orbital spacecraft constellation, keeping herewith the unity of the model, methods and algorithms. 
Ezrokhi Y. A., Kalenskii S. M. The mathematical modelling methods for inflight definition of the degradation of the gas turbine engine components performance . Trudy MAI, 2022, no 123 During the operation of the aviation gas turbine engine (GTE) its component technical state worsens continuously. It leads to degradation of the GTE main parameters, first of all, the engine trust and the specific fuel consumption.
Therefore the problem of the diagnostics of the gas turbine engine and its components during their operation is very actually, and its decision makes it possible to define authentically enough "critical" degree of deterioration of GTE components when their repair or replacement is necessary.
This problem is especially claimed, if there is a possibility to carry out engine components diagnostics not only during special separate ground tests, but inflight operation in engine system.
The offered diagnostics way is based on an assumption that influence of efficiency change δη_{i} of each taken separately turbojet components on its trust are independent among themselves and has linear character.
In this case it is possible to present the relative change of the engine trust δR as the sum of products of relative deviations δη_{i} on the influence parameter В_{i} of the engine components efficiency on the trust change.
The numerical indicators of deterioration of separate engine components efficiency received according to a presented method can be used for the analysis of the reasons of engine trust loss during its operation and for to work out losses indemnification methods.
Also these methods can be used for definition of the engine components state necessary at transition to modern strategy of management by a GTE resource  operation according to a state.
The example of definition of the change of engine components efficiency for a two shaft turbofan engine with the typical level of parameters corresponding to 4 generation is considered. 
Morozov A. Y. Adaptive interpolation algorithm for solving problems of celestial mechanics with interval uncertainties. Trudy MAI, 2022, no 123 The presented work performs the application of the previously developed adaptive interpolation algorithm to the problem of XF11 asteroid motion simulation with regard for the interval uncertainties in the asteroid position and velocity. The XF11asteroid motion around the Sun is being considered without accounting for the effect of the other planets. The original problem is formulated as a Cauchy problem for a system of ordinary differential equations (ODE) with interval initial conditions.
The essence of the adaptive interpolation algorithm consists in plotting for each time point piecewise polynomial function that interpolates the dependence of the solution to the problem on the point values of the interval parameters. An adaptive grid is being created over the region of the parameter uncertainty. Each node of the grid corresponds to the original problem solution with the parameters values determined by the node position in space. The grid adaptation is being performed depending on the interpolation error. In the places where the error is large, new nodes are being added, and in the places where the error is small, the grid is being rarefied.
The article presents the description of various existing methods and corresponding software libraries, such as AWA, COZYVI, RiOT, verifyode, for solving this class of problems. Employing the adaptive interpolation algorithm, the obtained interval system of ODEs is numerically integrated and compared with known results from the standpoint of the interval estimates accuracy and computational costs. Application of the fundamentally different approach to solving interval problems, allowed the adaptive interpolation algorithm obtaining solution boundaries with controlled accuracy. The algorithm is not subjected to the wrapping effect, and runs orders of magnitude faster than its analogs. 
Kondratieva L. A. Analytical approximation of inertial manifolds for the satellite motion model. Trudy MAI, 2022, no 123 
Zheleznyakov A. O., Sidorchuk V. P., Podrezov S. N. Simulation model of the system of maintenance and repair of electronic equipment. Trudy MAI, 2022, no 123 Simulation modeling is one of the most effective tools for studying complex systems today. Imitation is a kind of means of reproducing phenomena, just as a model is an abstract description of a system, object, phenomenon or process. That is, modeling is such an abstract form of reflection of reality, in which certain properties of the proposed objects are represented in the form of an image, a diagram, a plan, or a complex of equations, algorithms and programs. The use of simulation modeling in many fields of activity has a number of undeniable advantages. Firstly, it is an experimental method of cognition, which is a simple and visual tool for analysis. It helps to find optimal solutions to problems and gives a clear idea of complex systems. The advantages of this method are: simplicity, visibility, cheapness (compared to the experiment with recreating a real model), speed and convenience. The article provides a brief analysis of existing simulation models of complex systems in various environments. Due to the increased technical complexity of onboard equipment installed on aircraft, there is a problem in highquality and timely maintenance and repair, therefore, when organizing these types of activities, it is necessary to take into account a large number of factors that can affect the timing and quality of work. To solve these problems, on the basis of generalized statistical information about failures, the AnyLogic system has developed a simulation model of the process of organizing, functioning and repairing blocks with all the external and internal conditions affecting it, which allows making a rational decision about choosing a repair site, assessing the workload of specialists when performing various types of work, as well as forming requirements for the rational composition and quantity of spare parts of aircraft products required for operational restoration of operability. 
Dementiev A. N., Klyuev D. S., Novikov A. N., Mezhnov A. S., Peterskova Y. A., Zakharova E. V., Dementiev L. A. Мodel of the process of assessing the electromagnetic compatibility of the onboard equipment of the aircraft. Trudy MAI, 2022, no 123 As of now, the problem solution on spacerocket technology (SRT) application is impossible without radioelectronic means (REM) employing. This fact leads to the radiofrequency space oversaturation with electromagnetic radiation in the whole frequency range. The main causes, requiring effectiveness enhancing of the frequency spectrum employing and providing the REM joint operation under conditions of restricted spacetime and frequency resources are:
 Expansion of the scope of the REM application for the SRT;
 Increase in their power and number;
 Sensitivity growth of radio receiving equipment;
 Impact of the great number of jamming sources on the REM
Problems of assessing electromagnetic environment (EME), and determining various electromagnetic compatibility (EMC) characteristics occur while the RST REM operation. Thus, the search for new ways of ensuring the REM joint functioning with the specified quality under conditions of limited frequency, time and territorial resources is uptodate.
The EMC tasks consist in the following:
– establishing regularities for the optimal application of the radio frequency fields being created for information transmitting and/or receiving or extracting;
 establishing regularities of undesirable interaction of simultaneously functioning REM;
 identifying the ways and developing criteria and methods for the radio frequency space maximum application efficiency and capacity, including operationaltechnical characteristics of the REM, affecting the REM EMC;
 synthesizing the REM with the specified characteristics of the radio frequency spectrum (RFS) application, i.e. the characteristics, which include accounting for both outofband and stray radiation, and side reception channels.
With the scores of the onboard equipment with various characteristics and widely ramified onboard cable network (OCN) on the SRO, solution of the above said tasks relative to their interaction is of utter importance while the SRO development and manufacturing.
This will allow:
 analyzing the EME onboard the RST objects;
 evaluating the EME level with account for the frequency and spatial separation of the onboard equipment and OCN;
 determining the ways to EMC ensuring of the OE and OCN under specific operating conditions;
 simulating the processes of the electronic equipment functioning under complex EME.
This set of techniques and algorithms novelty consists in solving partial problems with the subsequent comparison of the obtained total values of the electric field strength at the specified points of the RST object, and the voltage induced on the OCN cables with the specified requirements, according to the developed techniques. 
Azarov A. v., Karavaev M. N., Rozhkov S. S., Slavyansky A. O., Smolka K. A. Synthesis of the aircraftbased phase direction finder. Trudy MAI, 2022, no 123 The aim of the work is to create a smallsized passive radar complex for placement on an unmanned aerial vehicle.
The principles of construction of a radio direction finder operating in the range from 1 to 18 GHz, limited on weight and size characteristics, are considered. A direction finder with a different number of antennas (from three to five) was simulated.
An antenna system is proposed that provides a high probability of obtaining an azimuth to a radio source with an accuracy of up to one degree in the viewing area up to 180 degrees with elements representing a combined spiral antenna consisting of printed, hemispherical and cylindrical spiral antennas using plates of radioabsorbing material. Laboratory models of antennas were created and measured. A comparative analysis of the characteristics of the mathematical model and the antenna layout created by 3D printing was carried out, according to the results of which it should be noted the high efficiency of the manufacturing method used due to the high repeatability of the results, low cost and high speed of sample production.
When placing a passive radar complex on a UAV, it is possible to determine not only the direction to the radiation source – its angular, but also geographical coordinates, and hence the range to the source of signal. The calculation of several bearings on the source of signal from different points of the UAV trajectory spaced in the plane allows us to solve the problem of locating it using the maximum likelihood method based on a set of measurements of bearings on the source and UAV motion parameters (angle measurements and altimeter information). 
Muratchaev S. S., Volkov A. S., Margaryan R. A., Bakhtin A. A. Development of an adaptive version of the OLSRV2 routing protocol in MANET networks. Trudy MAI, 2022, no 123 In this section, the results of simulation modeling of a MANET network based on the OLSR routing protocol were demonstrated. Two versions were taken: the standard OLSR routing protocol and the energy efficient OLSRv2 routing protocol, as well as the reactive AODV routing protocol. The developed algorithm for selecting routing protocols based on channel metrics was also implemented in the NS3 simulation environment. Simulation was carried out for various speed parameters, as well as for various network density parameters. When developing the algorithm for selecting routing protocols, the standard formats of broadcast data packets were changed to be integrated into the overall structure, since the algorithm involves switching between routing protocols based on the current network metric.
First of all, to test the operation of the energyefficient algorithm in the model, a comparison was made of the residual energy parameters in the network models. Thanks to the energyefficient algorithm, the developed network model with an energyefficient protocol saves more residual energy than a model with a standard routing protocol.
The simulation results are presented in the form of diagrams demonstrating the effectiveness of the modified protocol over the standard one in terms of network lifetime and packet delivery rate, as well as average delay. In a scenario with low node mobility, there is a 7% increase in the parameter compared to the standard routing protocol. When analyzing the results of simulation modeling, scenarios were identified in which the developed algorithm outperformed classical routing protocols in terms of average delay and data packet delivery rate. Also, a drawback was identified associated with a large number of added metrics, which leads to an increase in the number of generated service messages in the network. However, due to the stability of the protocol and its efficiency in various simulation scenarios, these shortcomings are compensated by parameters based on the residual energy in the nodes. 
Buzhin I. G., Antonova V. M., Mironov Y. B., Antonova V. A. Analysis of hazardous events and vulnerabilities of 5G transport communication networks. Trudy MAI, 2022, no 123 Being compared to the 3G and 4G, the 5G network offers significant increase in datatransmission rate, delay reduction and highreliability connection. These advantages will allow organizations to operate more effectively, as well as render services quicker, enhancing their quality. Data throughput of the fifthgeneration networks is higher, thus, connection of comparatively greater number of users and devices is possible.
The most serious safety hazards facing consumers and enterprises in the 5G networks are as follows:
1. Significantly larger surface of attack.
2. Severe aftermath caused by cyberattacks.
3. A potential for more aggressive spying.
4. Subscribers' activity monitoring attacks.
5. Dangerous DDoS attacks.
Let us consider the 5G/SDN/NFV possible vulnerabilities classification. Vulnerabilities occurring due to the insufficient organization of information technical protecting from the unauthorized access and technical channels of information leakage are beyond the scope of the system under consideration. In general, the SDN/NFV security ensuring issues are considered in [1, 2, 3, 4, 5, 6]. They are:
• Software vulnerabilities.
• Vulnerabilities caused by the presence of a softwarehardware bug in the 5G/SDN/NFV equipment [7].
• Vulnerabilities of network interaction protocols implementation and data transfer channels (IP, OpenFlow, etc.) [7].
• Vulnerabilities of the information security tools (the ones in the form of PNF, VNF), software and hardware.
Let us adduce a possible information security threats (IST) classification [7]:
• The IST by the information type being processed in the system:
– voice information;
– information processed by technical means of information processing;
• The IST by type of possible sources:
– an external intruder;
– an internal intruder;
– malware;
– a hardware bug (embedded or standalone) (not considered in this model).
• The IST by type of the information security property that is violated:
– information confidentiality (leakage, interception, capture, copying, theft, provisioning, distribution);
– information integrity (loss, theft, destruction, unauthorized changes);
– information availability (blocking);
– accountability of processes;
– repudiation of information or actions.
• The IST by the system type: since the 5G/SDN/NFV refers to the class of distributed 5G/ SDN/ NFV connected to the international information exchange network, threats specific to this type of system are considered.
• The IST by type of implementation:
– implemented through special impacts (of mechanical, chemical, acoustic, biological, radiation, thermal, electromagnetic nature) (not considered in this model);
– implemented through leakages from technical channels (not covered in this model);
– implemented through unauthorized access to the 5G/SDN/NFV;
• IST by type of the vulnerability utilized:
– related to the use of software vulnerabilities (hypervisors, virtual features);
– associated with application vulnerabilities;
– implemented through hardware bugs (not covered in this model);
– related to vulnerabilities in network protocols and communication channels (IP, Openflow);
– the ones the implementation of which is possible due to the vulnerabilities related to the gaps in the technical protection of information from unauthorized access (not covered in this model);
– implemented through vulnerabilities associated with the technical channels of information leakage (not considered in this model) [10];
– related to the vulnerabilities of information security tools;
– manmade threats.
• IST by type of the object being affected:
– information processed at the automated workstations of the system administrator and user;
– information processed in peripheral processing equipment (printers, plotters, remote monitors, video projectors, sound reproduction equipment, etc.) (not covered in this model);
– information transmitted through communications channels (while transmitted, while processed);
– information processed within the 5G/SDN/NFV virtual infrastructure and that includes storage;
– applications;
– software providing the 5G/SDN/NFV operation (SDN/NFV units, virtualization tools).
Considering the possible consequences of the IST implementation, we should focus on violating the key properties of information to ensure its security: confidentiality, integrity, availability, accountability, nonrepudiation. 
Podstrigaev A. S., Smolyakov A. V. Experimental investigation of the multisignal timefrequency parameters estimation accuracy in the digital receiver with subnyquist sampling. Trudy MAI, 2022, no 123 The modern cognitive radio systems and the spectrum monitoring devices used in spectrum management have to perform wideband signal analysis. One of the ways to achieve a wide instantaneous analysis band is to use a multichannel subNyquist receiver. Such a device receives signals from the many Nyquist zones and analyzes their aliases in the first zone. By aggregating information from the several independent channels having different sampling frequencies, it can disambiguate frequency measurements. However, due to such a receiver’s extensive analysis band (up to several dozen gigahertz), time overlaps of the input pulses become inevitable and regular events. Therefore, investigating timefrequency parameters estimation accuracy in the subNyquist receiver processing multisignal input gains great importance. The particular interest arouses the case in which the input signals are in distant Nyquist zones.
To perform the described investigation, we developed and built a subNyquist receiver prototype. As a source of the input for the prototype, we used two microwave signal generators connected to the prototype through the microstrip power combiner during the experiment. The first generator formed a pulsed signal and swept its carrier frequency, and the second generated a continuous unmodulated signal with a fixed frequency. We chose the frequencies of these two signals, so they were several Nyquist zones far from each other, but their aliases in the first zone were close.
The experiment showed in the example of 1 microsecond wide pulses that the frequency estimation accuracy remains almost the same in the cases of onesignal and multisignal input. However, the pulse width estimation error grows significantly for the multisignal input due to the receiver mixingup signals having close aliased frequencies. At the same time, the effect disappears entirely if the signals’ aliases are 20 MHz or farther from each other.
Nevertheless, we consider the errors estimations and the receiver’s frequency resolution obtained using the prototype enough for the vast majority of the wideband analysis tasks. Moreover, further errors reduction is possible through a runtime changing of the sampling frequencies and the fast Fourier transform width, and through the SDR techniques. Such techniques may include postprocessing based on signal accumulation, softwaredefined processing methods, and tunable bandstop filters at the receiver input suppressing the powerful interfering signals.
It is also worth noticing that most of the described in the paper effects related to the processing of the multisignal input do not result from any inherent properties of the subNyquist receiver. One can equally observe the same effects in the receivers with narrowband signal processing. 
Belskiy A. B. Requirements for onboard opticalelectronic means of aerial reconnaissance of aircraft. Trudy MAI, 2022, no 123 The need for roundtheclock, allweather and safe execution of combat and special missions by military aircraft, ensuring full situational awareness of the crew of the aircraft in the cockpit and the background situation under conditions of enemy information countermeasures impose increased requirements on airborne reconnaissance assets, namely on the functional characteristics of airborne monitoring, detection and recognition of targets, as well as determination of their coordinates and target designation
Airborne reconnaissance (monitoring) is carried out by special airborne technical means of reconnaissance of the aircraft, providing acquisition, registration, indication, processing and transfer of necessary data on objects and target environment.
Technical reconnaissance facilities include radar, radiotechnical, and optoelectronic systems operating in various spectral wavelength ranges, independently or together in various combinations.
Opticalelectronic systems are the most effective means for solving air reconnaissance tasks and obtaining information about the location and types of enemy objects due to their passive operation mode and high level of image resolution of targets (objects), including in complex backgroundtarget and operationaltactical environments.
The article discusses and analyzes the features of creating onboard optoelectronic systems to expand the capabilities of onboard optoelectronic systems for conducting aerial reconnaissance: building a system based on functionallyconstructive unified subsystems and modules; multichannel; using a hyperspectral channel for detecting, recognizing hidden, disguised objects; intellectualization of functioning; integration of individual subsystems and channels; automation of the processes of mutual alignment of channels, builtin monitoring and troubleshooting; automatic tracking of areal, point objects, with the allocation and further tracking of several targets; stabilization of the line of sight; interfacing with sensors for obtaining heterogeneous information; application of digital information processing methods; generation of output data from various sensors for processing and solving recognition problems; ensuring group interaction as part of the various control circuits. 
Sokolov D. Y. Application of artificial neural network for solving problems of forecasting the movement of ground objects. Trudy MAI, 2022, no 123 The article deals with considering the artificial neural network application for solving the problems of the groundbased object motion predicting. It proposes a new approach to the neural network architecture elaboration and applying its training techniques as applied to the specifics of the problem of motion trajectory prediction in the space of parameters. Estimation of various training techniques is given, and optimal parameters of coefficients, employed in the neural network training algorithms are determined.
The task of the groundbased objects motion predicting is uptodate as applied to both combat helicopters actions, in the case of their aiming at a moving maneuvering target, and civil aviation, including unmanned aircraft, when it is necessary to track various ground objects.
Application of the known types of neural networks for solving the problem of the motion predicting of a ground object (as an image of the object trajectory en masse) does not account for the sequence of passing the trajectory points by the object, which is an important information for solving the problem of the object motion predicting. Additional data processing and mathematical transforms allow solving the problem of accounting for the information on the sequence of passing points. However, this increases the overall complexity of calculations and may level the effectiveness of NN application for solving the forecasting problem.
The article proposes a certain architecture for a neural network building, in which each neuron corresponds to a separate point or region of space where the movement of an object being performed. This architecture assumes elaboration of a recurrent neural network, which imposes certain specifics on the training process and subsequent application of the neural network. Thus, the training process of a recurrent neural network should be iterative until a certain minimum of the objective function is reached.
The article discusses various ways of a neural network training and determines the most suitable ones from the standpoint of minimizing the errors and duration of the training cycles.
This article considers the movement in two coordinates (on a plane). However, in the general case, the space of parameters, in which the movement occurs, may contain greater number of coordinates (hyperplane). Both training and application of predictive neural network for the motion prediction in the space of parameters with any number of coordinates will be realized by the technique similar to the one for the motion on the plane.
In the prospect, the proposed version of a neural network building may be applied to predict the movement of various objects, including the abstract ones in a multidimensional hyperspace of their parameters. 
Anan’ev A. V., Ivannikov K. S., Kazhanov A. P. Model of the aviation target destruction process based on nonstationary markov random processes. Trudy MAI, 2022, no 123 The analysis of existing approaches to the assessing effectiveness of the aviation destructive means application is carried out in the article. It was shown that during the assessing effectiveness required release determination can be carried out both without and with taking into account the means of enemy air defense, which is substantiated in general. At the same time, the attention is focused on the fact that in case of the probability approach employment in different calculations, the probability in models of aviation destructive means application is assumed to be constant in many sources. The current state of affairs is inconsistent, because as the air strikes are delivered, the error correction is done by the aviation complex crews on the one hand, and the opposing side increases the counteraction by air defense and electronic warfare application, or by withdrawal of the forces and equipment from the attack.
The application of a mathematical model based on nonstationary Markov random processes is proposed with the aim of efficient combat aviation application and taking into account the alterations in the defeat probability assessment. Considering the alteration probability in air strikes cycles in this case consists in its representation as a variable quantity depending on time, which is the main difference between the proposed model and known approaches.
In this article a new approach to the effectiveness assessment of the aviation destructive means application is proposed. That approach takes into consideration alternating the probability of different ground (sea) objects destruction during air strikes cycles. Based on calculations of the obtained differential equations employing numerical methods the comparative analysis of the results acquired by using the known techniques and the new approach proposed was carried out. The account of the alteration probability is carried out by introducing a time dependence of probability, which allows determining required release of aviation destructive means, according to the alternating from cycle to cycle combat application conditions. The proposed mathematical models of the aviation target destruction process based on nonstationary Markov random processes, have significant universality and can be extended to a wide range of tasks. 
Kurennykh A. E. Software development for the integration of decision support models. Trudy MAI, 2022, no 123 The article deals with the issues of decision support and development of recommendations using computer modeling and methods for increasing the consistency of judgments, as well as issues of integration between information systems. The method for using sets of parameters and results of computer modelling in the process of multicriteria evaluation of alternatives is proposed and formalized. This paper regards a possible solution to the problem of usage of simulation models in the process of decisionmaking support carried out with enterprises information systems. The integration of simulation models and models of decision support is settheoretically formalized. Developed software form a separate module in the decision support system that makes it possible to rank alternatives submitted by simulation models. Designed architecture allows applying this approach for variable scientific and technical civil and military problems due to its universality.
In addition, in this paper the author formalized and developed mathematical and software to improve the consistency of judgments on the example of the method of paired comparisons, providing a sketch for an effective method to increase the consistency of judgments in a pairwise comparison matrix. Initially, there were identified criteria that are of great importance for experts who make judgments and then proposed a multicriteria optimization task and a way to solve it. Basically, the method is based on wellknown properties of matrixes containing paired comparisons marks, such as transitivity of judgments or consistency index for example. The use of both methods: integration of computer models and judgments consistency allows carrying out multicriteria analysis effectively with high precision. 
Knyazev A. S., Antonenko A. S., Arbuzov E. D., Chebotaryov A. D. The use of a multifunctional aircraft indicator simulator in the educational process of the university. Trudy MAI, 2022, no 123 The experience of education program mastering by the students of aviation universities reveals that constant contact, physical or visual, with aviation engineering is necessary for apprehending the operation principles of the aircraft aggregates and systems. In some cases, training becomes extremely difficult or ineffective until the aggregates and systems being described are shown in operation, in progress. The educational material presentation employing posters or slides with diagrams, graphs and static images does not allow the students to form an understanding and perception of the material being presented to the full.
The cockpits of modern aircraft are equipped with multifunctional indicators (MFI), through which the crew interacts with the onboard complex. Working with the MFI prior to the flight allows making a flight route, enter the targets coordinates, landmarks, and radio beacons. Application of the MFI in flight allows the crew to solve the tasks of piloting, navigation and combat employment, providing the necessary information for this. In this regard, it is necessary to pay more attention to learning how to work with multifunctional indicators when mastering modern types of aircraft.
The best way to learn is training on real technical facilities. An alternative option consists in employing aviation simulators. However, they are rather expensive and require qualified maintenance. Besides, their placement requires a separate area in specially equipped premises with electric power and/or hydraulic power installations, as well as other necessary equipment.
The article considers the issue of obviousness and effectiveness increase of cadetpilots training by employing separate cockpit element simulator in the educational process, namely multifunctional indicator, which allows cadets to choose necessary practical skills for working with the onboard equipment complex.
To introduce the MFI simulator into the educational process, information frames of the central information system (CIS) of the DA42T aircraft were reproduced. The content of the developed CIS frames on the MFI simulator reproduces completely the indication in the DA42T aircraft, contributing to the training quality improving and developing practical skills for working with CIS through the MFI in a real object (DA42T aircraft). The obtained results of the work can be employed further to develop simulators of multifunctional indicators for other aircraft types. 
Lukin V. N., Chechikov Y. B., Sekretarev V. E., Dzyubenko A. L., Altukhova N. F. Problems of maintenance of software and hardware systems. Trudy MAI, 2022, no 123 This article discusses the problems associated with the complexity of maintenance of hardware and software systems in conditions of lack of time, expansion of the complex and updating of the element base. The purpose of this work is to reduce the complexity of the development and maintenance of the software complex, increase the reliability of programming. The objective of the research is to substantiate the approach to the construction of software and hardware systems in the paradigm of objectoriented programming, as well as its application to the construction of systems of various levels of complexity. This article analyzes external and internal problems affecting the life cycle of hardware and software systems for various subject areas. An approach to solving problems is a technology based on an objectoriented paradigm that includes the concepts of interfaces, abstract base classes, vertical and fan inheritance, virtual functions, polymorphism. Objectoriented programming technologies ensure the simultaneous functioning of existing and newly appeared devices without rewriting the system. A variant of the RT adaptive OS for connecting onboard equipment is proposed, which significantly reduces the development time of serial and individual products and increases their reliability. An example of the possible application of the proposed methodology in the field of automation of laboratory research in medicine is given and it is shown how, with a wide variety of autoanalyzer fleet, common architectural solutions make it possible to develop a basic laboratory model with the possibility of detailing for each device. The novelty is the use of an objectoriented approach in the development of a realtime operating system (RTOS), which reduces the time and complexity of developing serial and individual products. 
Sofin A. P., Fedorova L. A., Sudar Y. M. On the issue of the use of amorphous devices. Trudy MAI, 2022, no 122 Amoeboid movement application in robotic and transport devices is associated with partial repetition of movements existing in nature. Design of prospective devices with amoeboid thrusters will require the research based on the dynamic computations of the object. Mathematical model forming therewith depends directly on the device structure and established option of its movement. The main tasks needed to be solved while such kind of propulsor design are set. A cylindrical body rolling along a rough plane was selected as the object. The external forces applied to the cylinder are being reduced to the resultant vector, which, together with the point of contact, determines the plane of motion position. The device body contacts with the rough surface via the protruding pseudopods. Its orientation in space may be altered by the liquid volumes moving inside the rigid hull, which allows changing position of the point of contact with the surface and the resultant vector of external forces.
The device movement in one of the planes is being considered in the course of dynamic computation. With this, the limit values of the force under which contact of the cylindrical body rolling both without and with sliding is being exercised, are being determined. The other problem being solved is associated with determining characteristics of movement of mass center of the hull and its rotation relative to the axis passing through the center of mass center.
The numerical study results reveal the presence of characteristic sections of motion determined by the selected parameters of the problem. The performed computations accuracy corresponds to the model being used.
The complex of kinematic indicators should ensure the forming of requirements for the control laws for the device being developed. Devices with amoeboid propulsors may be considered as bodies with a movable internal mass.
In the prospect, amoeboid propulsors may prove to be more efficient means of motion and transportation compared to the conventional wheeled and rotary mechanisms. The extremely low impact on the environmental objects associated with low ground pressure and trifling atmospheric emission should be considered the most important advantage of the amoeboid aggregates application.
A detailed study of the implementation options for each method of movement points at the significant number of their variety, and they are fully dependent on the concrete conditions and functions being realized. Along with the typical ones, the presence of the variety of transitional and combined forms of movement should be accounted for. Modern literature analysis allows soundly consider that the next stage of the studies development related to the amoeboid devices creation seems to be application of a device with basic hull shape in the form of a sphere. 
Aslanov V. S., Neryadovskaya D. V. A tether system at the L1, L2 collinear libration points of the marsphobos system. Trudy MAI, 2022, no 122 The article considers one of the L_{1} or L_{2} collinear libration points application for a tether system deployment in the direction of Phobos in a plane circular restricted threebody problem in the MarsPhobos system. An orbital spacecraft by which one of the tether ends is being fixed is located in L_{1} or L_{2} collinear libration points and is being held in one of these unstable points by the low thrust of its engines. The equation of the tether system motion in the polar coordinates system was obtained for the tether of constant length, the equilibrium positions were found, and the dependence of the vibrations period on the tether length was determined. Comparison of approximate solution for the small angles of the tether deviation from the local vertical with the numerical one was performed. The article demonstrates that the system “fixed” either in both the L_{1} point and L_{2} has potential wells in cases when the tether is being directed towards the Phobos side. It was revealed that the dependencies of the vibrations period on the tether length for the L_{1} and L_{2} points were fundamentally different. Comparison for both L_{1} and L_{2} of approximate and numerical solutions revealed herewith that the vibrations amplitude remained constant in contrast to the frequency. The results of this study may be employed for the future space missions provision. Thus, for example, a space lift may be arranged in the MarsPhobos system, which tether will pass through the L_{1} or L_{2} libraion point. Besides, such lift may serve as an intermediate station for conducting studies associated with the space exploration around it, as well as a platform for the interplanetary flights. “Fixing” the tether system in the L_{1} or L_{2}collinear libration point of the MarsPhobos system will allow conducting remote studies of Phobos employing a vehicle with sensors, which will hover above its surface. 
Popov I. P. Types of mechanical power for harmonic vibrations. Trudy MAI, 2022, no 122 The purpose of the study consists in detailing the types of mechanical power while harmonic oscillations. Due to the irreversibility of thermal energy, its derivative takes only positive values. With this, derivatives can be taken of both potential and kinetic energy. Harmonic oscillations herewith at which the derivatives (instantaneous powers) are necessarily signchanging functions, which fundamentally distinguishes them from thermal power, deliver the most interesting case. The inductance coil magnetic field energy is the kinetic energy analog in electrical engineering, the capacitor electric field is the potential energy analog, and thermal energy dissipated by the resistor is the mechanical energy analog. The article shows that at mechanical vibrations not only signpositive thermal power develops but the signvariable reactive powers as well, which characterize the potential and kinetic energies reversibility. The active power is understood as the average value of instantaneous power over half a period, and reactive power is its amplitude value. The total mechanical power, on the one hand, is being described by the Pythagorean formula, and on the other hand, it is equal to the product of the rms values of the harmonic quantities. A feature of the complex representation consists in the fact that while the total power calculating, one of the multiplied vectors should be conjugate. The concept of mechanical reactive, active and apparent powers is a generalization of the corresponding concepts from electrical engineering, which is a manifestation of electromechanical dualism. 
Egorov I. A. Consideration of plastic deformations in the design of wafertype compartments. Trudy MAI, 2022, no 122 
Dobryshkin A. Y., Zhuravleva E. V., Sysoev E. O., Sysoev O. E. Vibrations of composite thinwalled cylindrical open shells. Trudy MAI, 2022, no 122 Structures with thinwalled open shells bear an optimal ratio of the internal volume to the area of the enclosing surface. Such shells application therewith has disadvantages, namely, they are very sensitive to the forced vibrations originating from the external forces, such as wind and snow loads, equipment operation, etc. The article shows the necessity to shell structures calculating on dynamic processes caused by the forced vibrations impact. A model for the circular vibration frequency computing of a thinwalled cylindrical composite open shell with hinged support was obtained. A numerical experiment was conducted to compare the results and determine the error between the obtained computational model and the proven computer aided calculation performed with the LiraCAD program. The effect of the number of longitudinal halfwaves on the circular vibration frequency of the composite open shell was determined. The numerical characteristics of the vibration frequency of thinwalled shells may as well change due to the extra inclusions on the shells, such as an orifice, reinforcing rib, an attached plate, etc. Experimental data testify that these changes are of nonproportional character, which does not correspond to the generally known results of theoretical studies. Thus, the structures analysis on the dynamic vibrations requires refined mathematical models development. The authors propose a new approach to the finitedimensional model creation – a form of solving the problems of vibrations of a shell, carrying a small attached mass. The mathematical model refinement led to better quantitative and qualitative results compared to the known analytical solutions. In their earlier works, the authors analytically and numerically showed that the frequency reducing effect does not depend only on the magnitude of the shape initial irregularities, as is commonly believed at present, but on the geometric and wave parameters of the shell as well. The proposed approach is generalized for the case of vibrations of shells of finite length.

Potanin D. V., Samokhin P. A., Zelenyi A. E., Yakovlev I. M., Samokhina E. A. Computer modelling of shock impacts influencing on flight consoles considering nonlinear properties of materials. Trudy MAI, 2022, no 122 The prediction of strength characteristics of flight elements at the initial stage of design is important for constructions subject in use to shock influences. This paper investigates dynamic loads and strength characteristics of flight control console at disclosure and latching of a console. These loads arise on the initial site of flight because of blow about an emphasis. Calculation is made in dynamic module finite element software based on the explicit method of integration of movement differential equations. Suggest calculation model considers friction between components. Friction is set between between plugs and an axis, between an emphasis and the console, and also between a stopper and the console. Elastoplastic properties of materials the most subject to deformation of assembly details are simulated with use of the diagram of plasticity. As a result of the simulation, the reaction forces between the most loaded parts of the assembly, the maximum flight console scope and fluctuations are defined. The period and amplitude of cross fluctuations of the console and longitudinal fluctuations of a compartment mean fluctuations. The stressstrain state of a console as a part of a flight compartment is investigated in the conditions of shortterm shock loading. Verification of calculation is carried out by means of comparison of modeling results with the values received at a natural experiment on disclosure of consoles by the pyrotechnic mechanism. The relative deformations of the emphasis and the compartment upon impact were measured by strain gauges. To register the rotation of the console, a video was taken. Good convergence of calculation results with a natural experiment is shown. Values received by a numerical method of calculation differ from results of an experiment less than for 8%. 
Baklanov A. V. The effect of the annular diffuser design on pressure loss. Trudy MAI, 2022, no 122 Despite the fact that random processes are ubiquitous, doubts remain as to how random they are, and whether this randomness is seeming, based only on the limitations of our knowledge.
If the uncertainty of the processes occurring at the quantum level is already largely beyond doubt, the stochasticity of macroprocesses, and turbulence in particular, is still a subject of scientific discussion, if only because they are described by deterministic equations.
The article shows that the NavierStokes equations used to describe hydrodynamic flows lose their deterministic properties when they are integrated by computational methods. This can explain the rather successful application of these equations in solving many practical hydrodynamic problems in the implementation of turbulent flow regimes. However, this approach to describing turbulent flows can be correlated rather with analog modeling of turbulence.
In order to describe both laminar and turbulent flow regimes in a controlled manner, the author proposes to consider the NavierStokes equations in the phase space expanded by introducing an additional variable characterizing the entropy production. For laminar flow regimes, the entropy production takes on a zero value, the additional term disappears, and the transition to the NavierStokes equations in their standard form is being realized.
The article considers the issues of the possibility of emergence and maintenance of nondeterministic, i.e. stochastic processes in a liquid due to the existence of incompatible between each other boundary conditions, as well as the ways of describing them relating to the turbulent flow. It is shown that the velocity profile of a turbulent flow can be described as a generalized solution of the problem, which is the sum of the two terms, each of which is the product of two functions: one of which determines one of the asymptotes of the solution, while the second one determines the degree of influence of this asymptote on the general solution in each point of the area of interest.
The plane Couette flow problem was solved by dint of this approach. Good agreement of the results with experimental data is demonstrated. 
Khatuntseva O. N. Finding a generalized analytical solution to the plane Couetta problem for a turbulent flow regime. Trudy MAI, 2022, no 122 Despite the fact that random processes are ubiquitous, doubts remain as to how random they are, and whether this randomness is seeming, based only on the limitations of our knowledge.
If the uncertainty of the processes occurring at the quantum level is already largely beyond doubt, the stochasticity of macroprocesses, and turbulence in particular, is still a subject of scientific discussion, if only because they are described by deterministic equations.
The article shows that the NavierStokes equations used to describe hydrodynamic flows lose their deterministic properties when they are integrated by computational methods. This can explain the rather successful application of these equations in solving many practical hydrodynamic problems in the implementation of turbulent flow regimes. However, this approach to describing turbulent flows can be correlated rather with analog modeling of turbulence.
In order to describe both laminar and turbulent flow regimes in a controlled manner, the author proposes to consider the NavierStokes equations in the phase space expanded by introducing an additional variable characterizing the entropy production. For laminar flow regimes, the entropy production takes on a zero value, the additional term disappears, and the transition to the NavierStokes equations in their standard form is being realized.
The article considers the issues of the possibility of emergence and maintenance of nondeterministic, i.e. stochastic processes in a liquid due to the existence of incompatible between each other boundary conditions, as well as the ways of describing them relating to the turbulent flow. It is shown that the velocity profile of a turbulent flow can be described as a generalized solution of the problem, which is the sum of the two terms, each of which is the product of two functions: one of which determines one of the asymptotes of the solution, while the second one determines the degree of influence of this asymptote on the general solution in each point of the area of interest.
The plane Couette flow problem was solved by dint of this approach. Good agreement of the results with experimental data is demonstrated. 
Berezko M. E. Influence of the choice of boundary conditions on the results of the calculation of wall mounted flows. Trudy MAI, 2022, no 122 
Maklashov V. A., Piganov M. N. Algorithm for determining the bias of coordinate estimates. Trudy MAI, 2022, no 122 The article deals with the methodology for determining the radio emission source location in the tasks of electronic reconnaissance. To determine the radio emission source location, the azimuth direction finding from the aircraft is employed. It is noted that the previously proposed model allows determining the source location, however, it requires the zones of uncertainty calculating. The article shows that the need to calculate the uncertainty zones is associated with the fact that the error ellipse, calculated during models operation, requires an unbiased estimate of the source coordinates. The unbiased estimation obtaining while triangulation is possible only in symmetrical geometries, when the triangle formed while position determining is close to the equilateral one. In all other cases an estimation bias (the mean coordinates estimation value deflection from its true one) is being observed. As far as it is necessary to have bounded area of the most probable location of the radio emission source, the problem of this area plotting comes into being. The authors developed an algorithm for determining the radio emission source coordinates estimation bias relative to their true values for the uncertainty zones computing while using triangulation method for its location detection. Modeling of the radio emission source location determining process was performed. It was suggested to employ the basic TargetLocation algorithm to obtain the output data. It realizes the triangulation method. With this, three steps should be performed. These are triangulation base size computing; determining angles of the triangle; computing the source relative distances from the bearing points; determining the target coordinates. Basic simulation stages were performed in MATLAB. The following procedures were executed herewith: computing correlation coefficient and mean square deviation of the target coordinates; computing semiaxes of errors ellipse and angles between the X axis and the main ellipse axis; correcting the errors ellipse sizes. Analysis of the simulation results was performed, which revealed that the method consisting in measurements sorting out and ellipse sizes correction by the bias value yields the uncertainty zone encompassing true position of the radio emission source. The authors established that the presented method allows increasing the location determining accuracy. The bias value largely depends on the tactical situation geometry. Thus, in practice, it is necessary to know either analytical dependence of this bias on the geometry and measurement errors, or possess the table of these values. To obtain the above said dependencies, a large series of experiments conducting is required. 
Kozlov K. V., Volkov A. P., Starovoitov E. I., Popov E. V. A fullwave simulation of onboard earth surveillance radar electromagnetic fields for an emc ensuring. Trudy MAI, 2022, no 122 The use of onboard Earth surface surveying radar (including SAR) solves a number of tasks, which include the survey of the underlying surface, obtaining radar images of the terrain with a required resolution, detection of natural and artificial ground objects, operational mapping, etc. The installation of radar on board an aircraft is associated with the layout of various equipment in a confined space, taking into account the requirements of electromagnetic compatibility. Due to the fact that the strongest source of electromagnetic interference on board of aircraft is the radar, the assessment of its impact on the operation of the rest of the equipment is of paramount importance. The peculiarity of the UHFband under consideration is that the wavelengths are comparable with the lengths of external and internal cable lines, as well as with the dimensions of the electronic equipment blocks. The paper presents the methodology of numerical modeling of the distribution of the electromagnetic field in the near zone, created by onboard radar of the UHFband, designed for Earth surface surveying. For electrodynamic modeling of the electromagnetic field's distribution, the authors used a Finite Difference Time Domain Method. An assessment has been made of the electric field strength and current density induced on the electronic equipment block's housings located next to the active phased antenna array of the radar. These data can be used in works on electromagnetic compatibility of onboard electronic equipment. A description is presented of laboratory research schemes and the sequence of complex checks of equipment on the aircraft, associated major challenges. The authors separately considered problems arising during testing of satellite navigation equipment. 
Titov K. D. Principles for constructing an ultrawideband communication channel on an unmanned aerial vehicle of a lightweight helicopter type. Trudy MAI, 2022, no 122 The article describes the relevance and state of development of an unmanned aerial vehicle of a lightweight helicopter type of the homeproduced “Grach” series. By reference to application specifics of the unmanned helicopter with a wide range radio reconnaissance station as a objective load application, the requirements imposed to the control and data transmission system place on it were formulated. The compliance of the installed system with the requirements is analyzed, and technical, economic and operational advantages of the communication systems based on ultrawideband signals are demonstrated. Based on the earlier studies, devoted to the issues of creating a lightweight helicopter type unmanned aerial vehicle, as well as generating, processing and studying ultrawideband signals, specifics and principles of a ultrawide band communication channel design, which determine technical appearance of control, data transmission and local radio navigation system being installed on the aerial vehicle were formulated. Technical characteristics of the control and data transmission system, associated with pulses generation and processing; the signals radiation, and noise immunity assessment of antennae systems; frequency range selection, signal width and type; the issues of the system placing on the flying vehicle, as well as assessing the possibility of local navigation system integration into the communication system were analyzed and proved. Inferences were drawn on the substantiated technical characteristics impact on the tactical characteristics such as communication range, flight time, takeoff mass etc. 
Smolyakov A. V., Podstrigaev A. S. Experimental study of the noise figure of the digital receiver with undersampling up to 18 GHZ. Trudy MAI, 2022, no 122 Due to the expansion of the frequency range and the number of emitting radioelectronic means in many scientific and technical fields, performing a wideband analysis of the signal environment becomes necessary. For this, one can use a multichannel undersampling digital receiver (USDR). Such a receiver estimates a signal carrier frequency by unfolding its spectrum in each channel from the first Nyquist zone to the subsequent zones. The unfolded spectrum components in each channel are then compared with each other. The goal is to find the frequency at which the components from all channels coincide. This frequency is assumed to be the true carrier frequency of the received signal and not its alias. In this work, we investigated the USDR prototype, which does not contain a lownoise amplifier (LNA) at its input. Therefore, the prototype’s noise figure (NF) is high and reaches 41 ... 52 dB. However, using an input LNA can significantly reduce the total NF of the device. At the same time, one should bear in mind that with an increase in the LNA’s gain above a certain value, the receiver’s dynamic range begins to rapidly narrow. The resulting frequency dependence of the NF in the 18 GHz band has significant nonuniformity (11 dB). Therefore, when creating wideband analyzers to reduce the sensitivity variation, it is advisable to use equalizers and amplifiers with compensating frequency dependences of the NF and gain. Using the USDR with characteristics similar to those obtained for the prototype, we can achieve a –125… –116 dBm sensitivity for the wideband analyzer. This sensitivity is high enough for the considered 18 GHz frequency band. 
Nikitin A. D., Ivliev A. S. Possible methods for controlling the output power of amplifier modules based on mtype devices. Trudy MAI, 2022, no 122 The article is devoted to the study of the operation of Mtype amplifiers in various output power control modes, to realize the possibility of multimode operation of transmitting modules of radar stations (RLS) on active phased array antenns using Mtype electrovacuum devices (EVD). The need for such studies arose with the increasing requirements for powerful transmitting modules. The results of studies of various methods for controlling the output power of the amplitron are presented. A fundamentally new way to control the output power of Mtype amplifiers is considered  control of the operating voltage with a change in the magnitude of the magnetic induction. As a result of the studies carried out on the possibility of operating Mtype amplifiers in the output power control mode, the following was revealed: when controlling the input signal, the range of output power variation is at least 1.0 dB;  when controlling the anode current, the range of output power variation is at least 5.0 dB;  when controlling the operating voltage, the range of output power variation is at least 5.2 dB. The results obtained can be of great practical importance in the construction of powerful transmitting amplifying modules for multimode radars with active phased array antennas and passive phased antennas array. It is shown that the use of a combined method of output power control, which combines the control of the input signal, anode current and control of the anode voltage, will allow changing the output power of the amplifier in the range of more than 11 dB. It was also shown that when controlling the input signal of the amplifier, it is possible to expand the operating frequency range of the amplifying module up to 1012%. 
Vorotyagin V. N. Method of structural and parametric configuration of the motion and navigation control system of a small space vehicle for remote earth sensing under different scenarios of destructive impacts. Trudy MAI, 2022, no 122 Today, methods and technologies employing Earth remote probing data being developed by Roscosmos enterprises allow suggesting unique ways for ensuring safety, increasing efficiency of exploration and extraction of natural resources, introducing the latest practices into agriculture, preventing and eliminating consequences of emergencies, as well as protecting environment and controlling climate change. The issue of new space technology developing (a small spacecraft for the Earth remote probing in particular) is becoming most relevant.
To increase the degree of the design decisions validity while creating a small spacecraft, the article considers:
 Conceptually new approach to the development of a scientificandmethodological apparatus for multicriteria selection of the onboard control system structure and parameter on the example of a small spacecraft motion and navigation control system;
 Optimization of its limited resources to ensure proactive compensation of destructive external agency impacts
The article presents the developed structuralandlogical scheme for motion and navigation control system configuring of the Earth remote probing small spacecraft. The proposed approach allows putting into practice a multicriteria selection of effective configuration options for motion and navigation control system of a small spacecraft with account for various types of structural redundancy of the onboard equipment, and a wide range of element base. The conceptual and mathematical statements of the problem are given, and an algorithm for multicriteria synthesis of the motion and navigation control system appearance of a small spacecraft is developed.
The proposed technique will allow, even at the spacecraft design stage, significantly reducing the number of design errors by the decisionmaker, as well as improving the quality and efficiency of the created space systems application. 
Anan’ev A. V., Ivannikov K. S. A dynamic model for assessing the effectiveness of scenarios for conducting aerial reconnaissance by an integrated spatially distributed reconnaissance aviation complex. Trudy MAI, 2022, no 122 Aerial monitoring (reconnaissance) piloted complexes application in the interest of operational strategic decisionmaking is of great importance for the State security ensuring. However, such complexes employing is often performed in extreme conditions stipulated by climatic (severe meteorological) conditions, the destructive effects of manmade disasters, the danger of air defense means employing by unlawful armed formations, conditions of armed hostilities waging, etc.
In this regard, the article proposes an integrated spatially distributed reconnaissance aviation complex, which, unlike the known ones, includes unmanned aerial vehicles, controlled by the onboard operators situated directly on the manned aircraft for waging and controlling reconnaissance (by air monitoring).
Application procedure of such complex has been considered for the most difficult case, namely aerial reconnaissance waging under conditions of armed hostilities while the ground situation disclosure two stages. At the first stage, under condition of radio signals receiving possibility, such as radio distress signal, radio signals of the survey targets etc., passive radio and radiotechnical reconnaissance is being waged with the technical capabilities of the piloted aircraft onboard sensors. At the second stage, supplementary reconnaissance and reconnaissance of the objects of interest is being performed by the optoelectronic and other means positioned on the unmanned aerial vehicles.
When proposing modernization of the aerial reconnaissance (monitoring) and basing on the system approach, it is important to apprehend how the solution being proposed will affect the system of a higher rank, namely executive, or, in a particular case, striking. For this, a dynamic model of the reconnaissancestrike actions process was developed. It represents a state graph with time and probabilistic parameters indication. The article shows the equations system solution based on the states graph in the form states probabilities time dependences. The article demonstrates the solution of the system of equations, which are formed on the basis of the state graph in the form of time dependencies of the probability states.
The proposed model wields significant commonality and may be propagated on the wide spectrum. 
Blinov A. V., Razumov D. A. The procedure of formalization of strategies as an element of the methodology for taking into account uncertainty factors in forecasting the indicators of the implementation of space technology development programs. Trudy MAI, 2022, no 122 In the process of space technology development programs realization, various factors affect the program activities and implementation indicators. Development of respective technique for the factors considering is required. The forecasts of programs realization are based on the variant basics.
The program realization strategies defining is the initial stage of the uncertainty factors considering while the program indicators forecasting. The realization strategies are being based on the goals and priorities of the State policy of the Russian Federation in the field of space activities.
The twolevel system of priorities is applied when defining strategies. The first level is strategic priorities based on the priorities of the State policy of the Russian Federation. The second level is the priority of the event within the strategic priority.
Program activities are being distributed among separate groups, affecting various properties of the program. When forming various options for strategies, a sequential search of the formed groups of program activities is used. The program activities priority is distributed by the Fishburn method according to the number of results achieved.
Possible strategy options are sequentially considered. Program activities are being ranked according to the degree of their impact on the contribution to various properties of the program.
The strategy under consideration will focus the allocated resources on the realization of a group of program activities aimed at achieving one of the properties of the program. The results changing of the program activities realization occurs due to the funding redistribution between the various groups activities. The funds of the lower priority groups of program activities are distributed in favor of the activities of the group with the highest priority.
Formation of groups’ priority of program activities aimed at achieving various tasks and properties is being performed. Further, the priority group's program activities are filled at the expense of the lower priority group, with account for the effect of the uncertainty factors. Funding redistribution of program activities according to the formed options of strategies takes place.
Sequential consideration of the the program realization options will allow selecting the most rational strategy. 
Bannikov A. V., Litovka Y. V. Computational and logical intelligent control system for a multicathode galvanic bath. Trudy MAI, 2022, no 122 The most important electroplating quality indicator is the uniform distribution of the applied metal thickness the on the part surface. It is advisable to process smallsize parts conjointly, since largevolume electroplating baths are being used as usual in industrial conditions. Accordingly, it is unprofitable to process one part in one operation cycle of the electroplating bath. Given that the shapes of the parts being processes may differ and the number of parts may vary, this or that parts’ placing on the special suspending device may lead to various values of the total unevenness. Besides, the ineffectual placing may cause significant metal losses and excess electric energy consumption. Accordingly, the task of such multicathode system optimal control comes into being.
The article considers a computationaland logical intelligent system for controlling electroplating applying on the multiplicity of the partscathodes. The computationaland logical intelligent optimal control system solves the problem of searching for the optimal placing of several cathodes of various shapes and weights in an electroplating bath to obtain coatings with minimal unevenness.
To solve the set problem, the developed system employs the full search method, modified Gomori algorithm and the branches and boundaries method. The initial data for one of the three methods selecting is the number and shape of the parts to be electroplated. Afterwards, employing both database and knowledge base, the best method for the problem solving being defined, and the problem solution of optimal partscathodes placing on the suspension from the viewpoint of the unevenness criterion is being solved. At each stage, the technologist has the ability to control the process of the task solving and result correcting.
As the result of the optimal control system application in electroplating production, the total unevenness of the galvanic coating on the surface of many simultaneously processed parts decreases; the parts processing speed increases; the number of defects in the production process decreases, and the load on the electroplating line operator decreases. It is worth noting as well the electrical energy consumption reduction by the galvanic line when implementing a computationalandlogical intelligent system for optimal control of the galvanic coating applying process employing a variety of partscathode of various shapes and sizes. The proposed Gomori method modification increases the control system efficiency and reduces the amount of time required to calculate the optimal parts placing on the suspension. 
Ezrokhi Y. A., Kalenskii S. M. Identification of gte mathematical model by test data. Trudy MAI, 2022, no 122 One of the important tools applied at all stages of the aviation gas turbine engine (GTE) life cycle is the mathematical modelling of GTE operation. Such the engine mathematical model (EMM) allows to calculation of its altitudevelocity and throttle performances to form the initial data for gas dynamic calculations and designing of GTE units, for control system design, for planning of various kinds of tests, carrying out of GTE diagnosis and also decisions of other problems arising during the GTE creation and operation.
Efficiency EMM at various stages of the engine creation depends on adequacy of the modelling to its real operation. In this connection increase of accuracy EММ is rather important problem on which decision the expediency and productivity of application EММ in the practice substantially depends.
The problem of ЕMM accuracy and adequacy increase can be resolved during some stages.
At the first stage the initial aprioristic EMM was analyzed by audit of basic equations, inequalities, logic conditions, and also approximating dependences about conformity to those physical processes for which they were got.
So, in particular, at this stage correctness of use in EMM the thermodynamic equations applied to enthalpy and temperature of a working medium and it thermo physical properties, approximating dependences for the unit performance (received in advance by means of independent tests or calculations) from the viewpoint of their interpolation and extrapolation from area of their preliminary settlementexperimental definition is checked.
Besides, correctness of the continuity equation on an engine flowing path (taking into account possible selections, leaks and supplies of a working medium), conservation of energy and an impulse, and also the laws of engine control (taking into account accuracy of regulation and limitations), defining fuel flow into the combustion chamber, position of the compressors guide vanes and jet nozzle door (if these elements are changed from a one mode to other) is checked.
Generally the method of EММ identification with the engine tests results is reduced to a finding of certain number of correction factors to conditionally constant EMM parameters (to units performance, the sections of a flowing path area values, values of selections and leaks of a working medium and another), capable of the least divergence of the settlement and experimental results. 
Zulfugarli P. R. New criteria for optimizing the functioning of imaging devices installed on highspeed unmanned aerial vehicles. Trudy MAI, 2022, no 122 Effective visual monitoring of the ground situation can be carried out using various imaging devices installed on the UAV. In this case, the spatial resolution can be up to 1 cm. The dominant direction here is the fulfillment of the criterion for overlapping images of each other, obtained at the rate of UAV movement. It is common knowledge. That in order to obtain a highquality orthomosaic image, adjacent terrain images obtained during the UAV flight should overlap 60% in the forward direction and 20% in the direction perpendicular to the direction of movement. At the same time, when the carrier is flying at supersonic speed and the requirements for the overlap of timesequential images are often not met. In such cases, qualitatively new criteria are required to optimize imaging systems. The resolution of photogrammetric images obtained from aircraft equipped with imaging devices is determined by such a metric as the Ground Sample Distance, or GSD for short, which is defined as the distance between two adjacent pixels.
With regard to highspeed flying objects equipped with imaging devices, the following optimization criteria have been proposed: (1) Design criterion α_1, (2) Functional optimization criterion α_2 The first criterion is put forward in order to achieve small design dimensions of the imaging unit for a given value of the number of pixels per unit image width and GSD = const. In turn, the second criterion is put forward from the conditions for achieving stealth devices for various detection systems. The solution of the formulated optimization problems showed that the criteria α_1 and α_2 are fulfilled with a square root dependence of the distance from the sensor to the ground object and the size of the sensor area on the focal length of the device, respectively. 
Aslanova A. B. Questions of optimization of the combined power supply of the UAV with the use of solar batteries and ground air transmission of energy by a laser beam. Trudy MAI, 2022, no 122 To ensure the reliable operation of the UAV, a promising solution is the wireless transmission of energy through specialized ground base stations. At the same time, such power supply systems are expensive and dangerous for the population due to the high intensity of the laser beam and excessive electromagnetic radiation. A partial solution to this problem is the joint transmission of information and energy from a single base station. There is also another solution to the problem  the use of solar panels. However, the effectiveness of such a solution is still too low. In this case, the power supply of the UAV can be carried out according to the following simple rule (1) If there is a cloud, then the power supply is carried out through ground base stations by sending highintensity laser beams; (2) If there is no cloud, then solar power supply is used.
The case of a cloudy sky is considered in detail, when the UAV, by definition, flies at the level of the lower boundary of the cloud cover.
The problem of finding the optimal height of this boundary with a constant height of the upper boundary of the cloud layer is formulated and solved. The corresponding algorithm for the implementation of the proposed method has been compiled. The possibility of optimizing the construction of combined power supply systems for UAVs by minimizing the total energy losses along the paths of their propagation is considered. The case of a cloudy sky is considered in detail, when the UAV, by definition, flies at the level of the lower boundary of the cloud cover.
The problem of finding the optimal value of this height with a constant height of the upper boundary of the cloud layer is formulated and solved. The corresponding algorithm for the implementation of the proposed method has been compiled. 
Krasnov A. M., Tregubenkov S. Y., Rumyantsev A. V., Khismatov R. F., Shashkov S. N. Methodology for estimating the efficiency of opticalelectronic systems using an analytical model. Noise model of the «Oesoperator» system. Trudy MAI, 2022, no 122 Efficiency assessment is an integral part of optoelectronic systems (OES) development stages, testing and operation. The lack of a unified technique for optoelectronic systems effectiveness assessing leads to the fact that various assessment methods are employed to compare different systems, which results in obtaining contradictory results that do not provide objective data for making appropriate decisions at various stages of optoelectronic systems life cycle. One of the ways to this problem solving consists in an analytical model developing, which will represent the basis for creating the unified complex of means for intellectual support for optoelectronic systems design and maintenance at all stages of the lifecycle.
The purpose of the presented article consists in describing an analytical model for the optoelectronic systems effectiveness assessing, in a part concerning the noise model of the “OESoperator” system.
The following noise components of the “OESoperator” system are considered: the noise variance of the visual system of the OES operator, and the noise variance displayed on the OES display. The article presents the formula dependences of the noise variance components displayed on the OES display. These are the spectral density of the noise on the display, the temporal noise bandwidth and the spatial noise bandwidth. A model for computing the temperature difference equivalent to the noise was considered.
Further, the article presents the example of the initial data presentation in the analytical model for optoelectronic systems effectiveness assessing, and the results of the noise impact assessment on such OES efficiency indicators as detection range, recognition and identification of an object.
The considered noise model of the “OESoperator” system as an integral part of the analytical model for optoelectronic systems effectiveness assessing is a tool for an objective assessment of the of the optoelectronic systems sensitivity, which excludes the subjective opinion caused by the human factor.
It is advisable to employ this noise model of the “OESoperator” system in the development of tactical and technical requirements for optoelectronic systems, and optoelectronic systems themselves at the preliminary and technical design stages.
Computing temperature difference equivalent to the noise allows performing assessment:
 Of noise components impact on the values of detection range, recognition and identification of the object to the specified tacticalandtechnical requirements at the stage products testing;
 Of the OES radiation receiver sensitivity for this parameter compliance with the values indicated in the specified in operational documentation at the stages of mass production and operation.
Thus, the noise model of the “OESoperator” system implementation, which is an constituent part of a single software package for intelligent support of design and maintenance of optoelectronic systems at all stages of the life cycle, was considered. 
Apollonov D. V., Bibikova K. I., Shibaev M. V., Efimova I. E. Creation of algorithms for the automatic control system of the convertible unmanned aerial vehicle. Trudy MAI, 2022, no 122 Convertible unmanned aerial vehicle called a tiltrotor is considered. Tiltrotor can flight airplane mode and helicopter mode by changing the propulsion thrust vector by tilting the axes of rotation of the engines. The tiltrotor has the ability to make a vertical takeoff and land, it can also perform horizontal flight at highspeed cruise. It is difficult to develop tiltrotor control system due to the variable characteristics of the UAV during flight. This paper describes analysis of methods for selecting controller parameters of control system regulators. When analyzing fault tolerance ensuring controllability imposes requirements on the choice of control laws in the angular motion control loop and trajectory motion control loop. In addition to the widely used PD and PIDcontrollers and the linearquadratic controller, algorithms based on the concept of the invers dynamic problem and fuzzy logic are considered. Results of research on the creation of algorithms for the automatic control system of a convertible unmanned aerial vehicle are presented. All the described methods were analyzed to ensure the robustness of the automatic control system in order to ensure the necessary quality of control in cases where the control object differs from the calculated one. In case of failure of individual elements of the system the characteristics of control object change during operation, this problem is also considered in this paper. A comparative assessment of various methods for implementing control loops for UAV trajectory and angular motion using proportionalintegrodifferential, linearquadratic, nonlinear controllers and the method of the inverse dynamic problem is carried out to identify the advantages and disadvantages of all these methods. 
Panteleyev A. V., Belyakov I. A. Application of the bioinspired optimization methods in the solar sail optimal openloop control problem. Trudy MAI, 2022, no 122 This article discusses application of bioinspired metaheuristic global optimization methods: Grey Wolf Optimizer (GWO) and Whale Optimization Algorithm (WOA) for the problem of optimal loopopen control. Optimal control needs to manipulate space probe with solar sail. These algorithms belong to the class of swarm optimization methods, which feature is possibility of data transfer between individuals. At the same time GWO and WOA were inspired by nature, therefore we may relate them to bioinspired category. The behavior of a nonlinear deterministic continuous model of a plant is described by a system of differential equations with given initial conditions and a nonfixed terminal time. It is assumed that only time information is available during control, i.e. the openloop control is used. Numerical solution is found in the form of saturation function, which guarantees fulfillment of parallelepiped control constraints. Function arguments are finding in the linear combination of given base functions. Since terminal moment is undefined, this article applies method of transformation to the fixed terminal time problem, which introduces new independent variable, related with time.
The task is to find optimal control law for realizing solar system mission flight from the Earth’s orbit to the Mercury’s orbit in the shortest possible time. Algorithm of two bioinspired metaheuristic optimization methods application and software were created for numerical solution solar sail openloop control problem. Software gives mathematical modelling with various parameters for a subsequent visualization. Comparison with known results was provided. Recommendations were provided for parameters choose to solve typical model optimization and applied solar sail control problem. 
Popov I. P. Umov integral vector, back impulse and other mechanical quantities. Trudy MAI, 2021, no 121 Due to the widespread application of advanced scienceintensive technologies in the space industry, these industries themselves are becoming a source of development not only of applied, but fundamental science as well. In this regard, Umov’s integral vector, backward impulse and other mechanical quantities in perspective may be of interest including the applied one. The said quantities are associated with the formal analogs of the Schrödinger equation (FAUSH). Formally, the Schrödinger equation (SH) induces the magnitude of mechanical motion of the zero order (in the sense that it is contained in the SH). It is noteworthy that the quantum mechanical design generates a macromechanical quantity. Obviously, other ACF can induce values of mechanical motion of other orders. The following theorem is proved: The following theorem is proved: the value of m_{e}v^{—1} in a hydrogenlike atom is quantized. The value of m_{e}v^{—1}, corresponding to the basic energy level is a fixed (unchanged) quantum. Almost all of the obtained results were a consequence of the quantum mechanical differential equations application, however, the results themselves are predominantly macromechanical. The mechanical motion quantities of various orders are being induced by formal analogs of the Schrödinger equation. These quantities include both known (mass, momentum, kinetic energy) and unknown (Umov’s integral vector for kinetic energy, backward momentum, etc.). In all FAUSHs, the orders of the partial derivatives differ by one. For quantities of motion with a positive degree of velocity, the order of the temporal derivatives is higher than that of the spatial ones. For mechanical quantities with a negative degree, the order of spatial derivatives is higher. 
Alimov N. I., Gorbulin V. I., Sudar Y. M. Formation of a family of trajectories of free spherical motion of a spacecraft as a rigid body, providing reorientation of its axis of dynamic symmetry to a given position. Trudy MAI, 2021, no 121 Analytical relations for trajectories parameters determining of the free (by inertia) spherical movement a satellite as a solid, which ensures reorientation of its dynamic axis of symmetry to the specified position in the regular precession mode, were obtained. A canonical inertial coordinate system, in which angles of orientation of the associated coordinate system, i.e. Euler angles, change in time linearly, was introduced. A peculiarity, explanating the ambiguity of determining the initial value of the rotation angle, is indicated, and the option of the pointed ambiguity elimination is suggested. The article demonstrates that spherical movement trajectory of a solid, which ensures the dynamic axis of symmetry retargeting to the required position in the predetermined time is a basic problem while reorientation control selection in the pulsing statement and computing required increment, kinetic moment and kinetic energy in the points of impulses application. The solutions being obtained allow assessing rather accurately the retargeting process duration and required energy consuming, necessary for further analysis. Besides, these solutions are a good initial approximation for the continuous control tasks. The authors introduced the notion of control strategy for spherical (angular) satellite motion control at lengthy time intervals, consisting of sequence of controls of the two active sections and ensuring transition from one angular motion trajectory to another, which kinematic and dynamic parameters are being determined based of the spacecraft flight program. The article proposes realizing continuous angular motion control computing at each active section based on the utilizing the concept of inverse problems of dynamics and algorithms for solving the problem twopulse control of the satellite reorientation. 
Korovaytseva E. A. Formation of a family of trajectories of free spherical motion of a spacecraft as a rigid body, providing reorientation of its axis of dynamic symmetry to a given position. Trudy MAI, 2021, no 121 The presented work studies opportunities of automatic segmentation method implementation for solving problems of axisymmetric static deforming of soft shells of revolution at large displacements and strains. Mathematical statement of the problem includes four quasilinear differential equations and nine nonlinear algebraic equations. Geometrical relations of thin shells nonlinear theory are employed herewith, and elastic potentials of various views are being engaged for nonlinear physical relations formulation. The opportunity of composite shell analysis is supposed, which corresponds to the statement of multipoint boundary problem. Algorithm of the parametric differentiation method is used for the problem solution. The initial relations of the nonlinear boundary problem are being differentiated herewith by the preselected parameter of the problem solving continuation. As the result, a system of interconnected quasilinear boundary and nonlinear initial problems is being formed. The result of the obtained system solving while studying shell deforming under conditions of large displacements and strains depends on simultaneous successful setting of a whole range of computational algorithm parameters. As far as the method of arbitrary search of parameters leads to irrational increasing the time of computer work with the program, the article suggests a reasonable setting of one of the algorithm parameters, namely, the number of segments into which the integration interval of quasilinear boundary value problem is divided. The said number of segments is being determined at the stage of preprocessing with the help of authored automatic segmentation method, which was successfully applied earlier when solving the linear boundary value problems. The article presents results of the three problems solutions on soft shell inflation by the pressure, uniformly distributed along meridian, using parameter differentiation method, one of the steps of which is the automatic segmentation method. Selection of inflation problem of a cylinder from MooneyRivlin material fixed at its ends by a roller is stipulated by the existence of this problem analytical solution. Three cases of arbitrary selection of a number of segments, into which the shell is divided, and a case of automatic segmentation are considered. The article shows that it is possible in the last case to obtain an optimal combination of solution accuracy and iteration processes convergence rate. The choice of a hemisphere inflation from neohookean material fixed along the equator by a roller problem is dictated not only by the existence of analytical solution of this problem, but also by the presence of singular coefficients in resolving equation system Jacobi matrix at the problem integration interval. The said feature leads to the fact that in a fairly large vicinity of the shell pole the condition, used as a criterion of shell division into segments, is violated in each point of the meridian. As the result, the number of segments determined by the automatic segmentation method appears to be quite large. However, the problem solution result turned out to be one of the best among the shell segmentation options considered from the viewpoint of both solution accuracy and iteration processes convergence rate. It is worth emphasizing that in both examples under consideration, one of the options of arbitrary setting of segments number lead to a principally unsatisfactory solution result. Thus, the automatic segmentation method application is necessary to obtain correct solution. The problem of inflation of a hinged hemisphere of neohookean material is selected as it does not have analytical solution. As the result of calculations, it was established that automatic segmentation leads to the lowest iteration processes convergence rate among all the shell meridian division considered options. Along with this, with insufficient number of segments the solution obtaining turned out to be impossible. The performed studies revealed that automatic segmentation method application was necessary for the computer groundless actions minimizing concerning the calculation algorithm parameters setting, as well as for the problem solution results accuracy and iteration processes convergence rate increasing. Along with this, when solving problems, which resolving equation system has singular coefficients at some point of integration interval, the said method application requires additional studies, and apparently, application of some auxiliary techniques. 
Korolenko V. A., Soliaev J. O. Evaluation of stress concentration around microsized holes within simplified models of strain gradient elasticity. Trudy MAI, 2021, no 121 This paper presents the results for the modeling of the deformed state and the level of stress concentration around the microsized holes. Analytical solutions are derived for the deformations of an infinite plate containing a cylindrical hole within several simplified oneparametric models of the strain gradient elasticity theory (SGET). Namely, we used the simplified strain gradient elasticity theory, the couple stress theory, the dilatation gradient elasticity theory and the fully symmetric GusevLurie theory, which all are the special cases of the general MindlinTupin SGET. Linear elastic isotropic behavior of the material is assumed. New variant of the PapkovichNeuber solution of SGET equations in terms of displacements is involved for analytical derivations. It is shown that this solution can be reduced to the standard Helmholtz decomposition for the gradient part of the displacement field and to the standard representation of its classical part. Based on the derived solutions we investigate the changes of the stress and strain state around the holes of different diameter. It is shown that the choice of a suitable variant of a simplified SGET model and identification of the length scale parameter for the certain materials can be performed based on the experimental data for the failure loads for the samples containing holes of different diameters (with a minimum size of ~100 µm). It is also shown that identification can be also carried out on the basis of direct methods of strain measurements around the smallsized holes, for example, by using digital image correlation methods, which requires the use of microscopy or, at least, macro photography techniques at the microscale level. 
Grishanina T. V., Guseva E. E. Method for calculating elastic vibrations of a cyclically symmetric structure. Trudy MAI, 2021, no 121 The article presents a new approach to the oscillation equations composing of elastic structures with cyclically symmetric structure. A cyclically symmetric elastic system is under consideration. At the k = 0, 1, 2, ..., N — 1 nodes of the system, located on a circle at equidistant points with angular coordinates of θ_{k}, the identic elastic rods of constant crosssection are being connected, working in tensioncompression, torsion and bendingshear in and out of the plane of the system. To compose the oscillations equations of the system, both displacement and rotation angles components, symmetrical with respect to the radial plane passing through the kth node, are being represented as cosine expansions in the circumferential direction, while skew symmetric ones are represented as sine expansions with wave numbers of n = 0, 1, 2, ..., N/2. Expressions of potential and kinetic energies for all elements of the system are being composed. With account for the cos nθ_{k} and sin nθ_{k} functions orthogonality conditions for different n on a system of equidistant points, the terms of these expressions for different n from the set of n = 0, 1, 2, ..., are being obtained uncoupled among themselves. As the result, the Lagrange equations in generalized coordinates for a cyclically symmetric system with 6N degrees of freedom disintegrate into separate groups of six equations for each number n being accounted for. Thus, the solution of the problem of a cyclically symmetric system oscillations of еру 6N order is being reduced to solving a number of problems for uncoupled subsystems of equations of the sixth order, representing separately harmonics n = 0, 1, 2, ..., ≤ N/2. 
Gyagyaeva A. G., Kondratov D. V., Mogilevich L. I. Derivation of the dynamic equation for a geometrically nonlinear plate interacting with a thin layer of a viscous incompressible fluid. Trudy MAI, 2021, no 121 At present, different methods for solving the problem of hydroelasticity are applied. They allow solving a set of problems in question be means of assumptions and limitations with a required precision and reliability. To make engineer decisions while examining hydroelasticity problems, specialized computer software is used. It allows simplifying the calculating process of hydroelasticity problems and demonstrating a graphical solution of the problems. Thinwall structures interact with viscous incompressible fluid, particularly plates and shell structures. They are used in machine industry, in instrument making industry, in aviation and space industry. Thus, one needs to build mathematical models and apply program systems to make decisions in designing machines and devices.The article consider the model of a mechanical system consisting of an absolutely rigid body (vibrator); an elastic rib, rectangular plate (stator) and viscous incompressible fluid. Using the Hamilton’s variation principle, the equation for the elastic geometrically nonlinear plate dynamics is derived. The mathematical model of the presented mechanical system consists of the incompressible fluid dynamics equations, the elastic geometrically nonlinear ribbed plate dynamic equations, the equation of motion for the absolutely rigid vibrator and the corresponding boundary conditions. The program for the analytical derivation of the dynamic equations for an elastic irregular nonlinear stator was developed. It takes into account the boundary conditions of a free support and the conditions of free fluid flow on the ends. The constructed mathematical model can be applied for the design of hydrodynamic supports. The mathematical model can be used in designing of hydrodynamic bearings that are operated in machine industry, in instrument making industry, in aviation and space industry. 
Zotov A. A., Nagornov A. Y., Volkov A. V., Popov V. O. Analysis of the dynamic characteristics of threelayer shells with discrete filler. Trudy MAI, 2021, no 121 The problem is posed to study dynamic characteristics of a threelayer cylindrical shell with the discrete filler, which is a regular system of coneshaped (or pyramidal) cells arranged in a checkerboard pattern. Threelayer structures in various technical objects often have a honeycomb filler’s structure are widely used. Despite the obvious advantages of honeycomb filler (low weight, high rigidity), there are circumstances that prevent their wider use. The closed cellular structure prevents the removal of condensate entering the internal space. And the complexity of ensuring and controlling reliable connection of the aggregate with the bearing layers (especially on curved surfaces) increases their labor intensity and cost. The proposed discrete structure largely allows you to solve the above problems. The design features influence of the of this threelayer shells type on the stressstrain state and stability under static loading has been studied in sufficient detail earlier. A complete solidstate and FEmodel of the investigated shell has been constructed. A modal analysis of the cell design was carried out as a next step, and then, having selected the zones of interest, the frequency response of the structure was investigated in order to plot the frequency response and frequency response. The NASTRAN solver is used to calculate eigenmodes and frequencies, the analysis type is set to Normal Modes / Eigenvalue. The geometry of the model was built using PLATE elements. In threelayer structures, the dynamic characteristics can be changed by varying the thickness of the bearing layers or filler and, thus, to obtain the optimal weight, damping, and also radiotechnical parameters. To determine the frequency response, a harmonic Frequency / Harmonic Response analysis is performed. It allows you to evaluate the response of the structure with a sinusoidal action. To assess the considering filler structure feasibility a comparative analysis of the dynamic characteristics between smooth and threelayer shells of equal dimensions material, was carried out. Based on the obtained results, it can be concluded that with an thickness increase, and, accordingly, the filler rigidity, the natural frequency decreases, however, with an increase in the bearing layers thickness, an increase in the values of the natural frequencies is observed. Also noted that main vibrations emanating from gas turbine engines are in the range up to 5000 Hz, and the coneshaped structure is preferable for use in places subject to dynamic loads. 
Malinin G. V. Methods of calculation of ribbed plates for strength and stability. Trudy MAI, 2021, no 121 The desire to increase the reliability of structures forces engineers and designers not only to turn to new materials, in particular composite materials, but also to the introduction of additional reinforcing elements that do not significantly affect the change in the weight of the structure. As such effective means is the use of stiffeners, which have become widespread in engineering practice. The foundations of analytical methods of structural mechanics applied to the problems of calculating ribbed plates and shells were laid by Russian scientists S.P. Timoshenko, I.G. Bubnov, P.F. Papkovich, V.V. Novozhilov, A.I. Birger. Currently, many scientists are also engaged in the calculation of ribbed plates and shells for strength and stability. In this paper, two analytical methods for calculating ribbed plates supported by a cross system of stiffeners are proposed: a method for calculating strength in determining the stressstrain state and a method for calculating stability in determining the critical load. The calculation of the stressstrain state and stability of the structures under consideration is associated with significant mathematical difficulties that an engineer can currently overcome with the help of modern mathematical packages. In this paper, the technique of strength analysis of the stressstrain state of a ribbed plate is implemented in the Mathcad package, and the stability problem is successfully solved in the Maple package. The calculation of the strength and stability of ribbed plates reinforced with ribs placed crosswise or parallel to one of the sides of the plate is considered. The proposed computational mathematical model is based on the replacement of the original ribbed plate with an equivalent flat isotropic plate. The stiffness characteristics of the equivalent plate are calculated taking into account the contribution of the reinforcing elements of the ribbed plate. It is assumed that the thinwalled structure is supported by a sufficiently large number of ribs located at a sufficiently small distance fr om each other, which allows their «smearing» relative to the median surface of the plate.Control examples of calculation according to the proposed methods are given. The results of analytical calculations are in good agreement with the results of numerical analysis performed by the finite element method in the MSC.Nastran/Patran package.The proposed methods will allow the engineer at the stage of preliminary calculation and design of the structure to identify the features of its stressstrain state, such as stress concentration sites wh ere it is necessary to reduce the size of the finite element grid during the refinement calculation in industrial packages of finite element analysis. 
Sposobin A. V. Meshless algorithm for calculating supersonic viscous gas flows. Trudy MAI, 2021, no 121 Тhe article presents in detail the algorithm for the numerical solution of the NavierStokes equations [12] by the meshless method [8, 10]. The described method is used for numerical simulation of blunt bodies flowaround by supersonic viscous gas flow [1, 2]. Cartesiangridbased immersed boundary method presented in previously published works was successfully applied to simulate such flows in the twodimensional planar and an axisymmetric formulation [3]. Numerical studies of the gas thermal impact change on the streamlined surface while the highly inertial particle motion against the incoming flow along the symmetry axis were performed by dint of it [4, 5, 6]. Particles motion along various trajectories required gasdynamics problems solving in the 3D formulation, for which the Cartesiangrid based methods application required too much computer memory. When solving gasdynamics problems by the meshless method, a finite sets of nodes is being selected in the space. Approximation by the least square method is applied for spatial derivatives computing in computational nodes. The said approach is being used for convective and viscous fluxes computing. The convection fluxes are being computed by the AUSMPW+ method in conjunction with the MUSCL scheme and van Abada limiter. The system of equations time integration is being performed by the explicit RungeKutta method of the third order of accuracy. The flowaround surface is being represented by the model of isothermal wall with the specified temperature. Conditions of gas adhesion, as well as pressure gradient equality to zero, which modeling also employs the least square method, is realized on the said model. The meshless method gives the opportunity to compute the gas flow in the areas with complex geometry, it is simpler in realization herewith compared to the finite volumes method, since it does not require generation of the highquality computational grid. It allows setting anisotropic distribution of nodes in space, which is of vital importance for qualitative resolution of the boundary layer near the flowaround surface. Along with the 3D realization, adaptation of meshless method for computing flat and axisymmetric viscous gas flows was performed. The software implementation of the described method is realized in the C++ programming language and employs the OpenMP technology for computations parallelization. A computational experiment was performed on modeling the sphere flowaround by the supersonic airflow at the Mach number of M = 3 and Reynolds number of Re = 10^{5} was conducted for the said method verification. The spatial shadow patterns of the flow, pressure field and Mach number are presented. Comparison of gas parameters in the boundary layer, obtained by the meshless method with the computational results of continuous flow combined with the boundary layer equations is presented. Correspondence of the gas computational parameters on the flowaround surface to the reference data and approximateanalytical expressions is demonstrated. The heat flow value in the critical point coincides with the one calculated with the Fay and Riddell formula, and the heat flow distribution curve along the surface is close to the approximateanalytical one. The next stage in the development of the meshless method is planned to solve numerically the unsteady multiphase flows problem, in particular, to simulate the solid particles motion in the shock layer. 
Bernikov A. S., Petrov Y. A., Sergeev D. V., Shtokal A. O. Depreciation of automatic spacecraft when landing on planets and their satellites, taking into account the elasticity of the landing device design. Trudy MAI, 2021, no 121 The spacecraft touchdown on the surface of planets and their satellites is one of the crucial flight stages. Since the planets surfaces are insufficiently studied, the kinematic parameters of the spacecraft movement may vary in a wide range. For the spacecraft shock absorbing while touchdown, landing devices are being used, which should ensure a touchdown with permissible overloads and a stable position of the craft on the surface. The landing gear consists of three or four supports, depending on the power scheme of the landing vehicle. The craft shock absorbing while landing is performed due to energy absorbers placed in the shock absorbers of the landing device. A rod, honeycomb, pipe and tape (flat rod) are being applied as singleuse energy absorbers, which absorb the energy of the craft while landing due to plastic deformation. The accounting for the landing device design elasticity will allow correctly determining the dynamic loads and stability area of the craft while landing, which is especially important when landing on comets or satellites with low gravity. When solving the problem of landing dynamics, the equations of motion of the landing gear supports are employed, with account for the elastic deformation of the structure. The regard for the elastic deformation energy accumulated in the elements of the landing gear and in the places where they are attached to the body will allow determining the dynamic loads on the apparatus and structural elements, as well as correctly determining the area of the apparatus stability to overturning. To determine the friction forces originating from the contact interaction of the heel of the landing device with the ground, experimental studies on the of friction coefficients measurement are being used. Tuff, basalt, foam concrete of different strength, sinter sand were being considered as analogous soils. AMG6 aluminum alloy, MA21magnesium alloy, and OT4titanium alloy were being considered as a material for the heel of the landing gear support. It follows from the experiments that for all combinations of rubbing metalground pairs, the friction process is oscillatory. When a spacecraft tpuchdown on bodies with low gravity, such as the Mars satellite Phobos, for which the acceleration of gravity is equal to df 0.005 m / s2, and even more so when landing on comets, for example ChuryumovGerasimenko, for which the acceleration of gravity is up to 80 thousand times less than on Earth, accounting for the elastic forces of the landing device design when solving the problem of landing dynamics is essential. On the «Rosetta» spacecraft, three landing gear supports contain clamping motors to ensure landing on a slope without tipping over, which is possible due to the energy of elastic deformation of the supports. When performing works related to soil drilling, the spacecraft must be securely fixed on the touchdown surface of satellites (comets). The clamping motors application here will be inefficient, since high axial forces are required while drilling, and the drilling time is rather long. In this case of touchdown, the spacecraft can be held on the surface with harpoons. 
Zagornyj S. V., Naumchik I. V., Dzitoev M. S., Mikhaylenko A. V. Exergetic analysis of elements of thermostating systems. Trudy MAI, 2021, no 121 The subject of the research is the regularities of changes in the thermodynamic parameters of thermostating systems of rocket and space complexes, depending on the composition of their equipment. The purpose of the work is to improve the thermostating systems of special RKK equipment to ensure the specified heat and cooling capacity, as well as temperature to ensure and maintain the accuracy and stability of their output parameters. The article presents the main results obtained during the study. The exergic analysis of thermostating systems for objects of rocket and space technology has been carried out. Research has been carried out on the possibility of using heat pump installations for thermostating objects of rocket and space complexes, which allows obtaining energy of a higher potential using lowpotential renewable energy from natural sources of heat or lowtemperature secondary resources. The expediency of including a vapor compression refrigeration machine into the thermostatting system based on a heat pump installation has been substantiated. Conditions are formulated under which the use of a heat pump will be more profitable than the use of a chemical heat source. A method of comparative analysis of a heat pump and a chemical heat source is presented, the results of which showed that direct heating consumes approximately twice as much fuel as heating using a heat pump. A schematic diagram of a universal allseason thermostating system based on a refrigeration and heating unit has been developed. The work performed is theoretical and experimental. The provisions outlined in the work are the result of the analysis and generalization of the research results of Russian and foreign scientists in the field of thermodynamics and heat transfer, the theory of heat engineering, the theory and practice of operating thermostating systems for rocket and space technology, as well as the results obtained in the course of research on the topic of research work of organizations industry and military scientific organizations of the Ministry of Defense of the Russian Federation. The main research results can be used both at the design stage in the formation of requirements for ensuring the specified heat and cooling capacity, temperature conditions and improving the level of thermodynamic efficiency of various objects of special equipment of rocket and space complexes, as well as to ensure the required values of the output indicators of the elements of thermostating systems at the stage exploitation. 
Buzhin I. G., Antonova V. M., Mironov Y. B., Antonova V. A., Korchagina A. S., Kanishcheva M. G. Exergetic analysis of elements of thermostating systems. Trudy MAI, 2021, no 121 AdaptiveMobile has identified a vulnerability in the of the Network Slicing mechanism implementation, which could disclose information about arbitrary network segments or cause a denial of service. The vulnerability was assigned the CVD20210047 number. Federal Service for Technology and Export Control (FSTEC of Russia) introduced vulnerability to the bank of threats and determined the level of danger as medium. One of the trends for this vulnerability elimination in the 6G networks is formulation of the classification principles and filtering of the 6G transport network traffic for effective application of the Network Slicing mechanism. The basic principles of collecting, filtering and traffic classification of the data transmission network are as follows:
The proposed principles and ways of solving the filtering and monitoring problem are aimed at eliminating the dangerous CVD20210047 vulnerability. 
Bakhtin A. A., Volkov A. S., Solodkov A. V., Sviridov I. A. A neural networkbased signal modulation recognition system implemented on a FPGA. Trudy MAI, 2021, no 121 In cognitive radio systems including softwaredefined radio, an important task is to recognize modulation type of received signals under various signaltonoise ratios in the communication channel. The detection of the modulation type in a received data packet can be used in ad hoc networks, as well as to provide dynamic spectrum access. To solve this problem, there are few common approaches, including the shape detection of the signal constellation, the study of the statistical characteristics of the signal, the use of deep neural networks and others. The use of deep convolutional neural networks leads to higher accuracy for large sets of different types of modulation. In addition, implementing the neural network on an FPGA allows not only changing the weights of the neural network, but also configuring the types and arrangement of layers without replacing the hardware component. The proposed system consists of hardware and software parts. The hardware part includes a Digilent Zedboard and an ADFMCOMMS3EBZ development board (based on an AD9361 configurable radio transceiver connected via an FMC connector). The software part of the system consists of the Petalinux distribution kit version 2019.1, the Linux industrial I/O driver, developed software for preprocessing the received signal and a 