Bibliographic references
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, http://mai.ru//upload/iblock/6fc/rgxmr6mmlslrhymdmfisr6uis3mr55de/03_Sedelnikov_Nikolaeva_Serdakova.pdf 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, http://mai.ru//upload/iblock/3c7/arubd5rfe830vm103ubnojssafu6yxb2/01_Popov.pdf 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, http://mai.ru//upload/iblock/ee1/1tkgzn4fg9nchax43cu3w9jrganc2vf1/02_Grishakin..pdf 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, http://mai.ru//upload/iblock/b3b/tj6n4imc93p4kyh13wxdziw3twpfrpe4/04_Feoktistov_Andrianov_Marin._1_.pdf 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, http://mai.ru//upload/iblock/f45/ybgmae4kclh3oaoritr1jrpwfo9r0q02/05_BogachevSergeev_idr_23.10.2023.pdf 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, http://mai.ru//upload/iblock/a55/vvfjvfguocczue27vyz9o49yh8hzsw3p/06_Pronina.pdf 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, http://mai.ru//upload/iblock/a88/wx2djgney6y10nvw2pbnrarodo3kkvwi/07_Sazanov_Pavlov_Pismarov_Matveeva._1__1_.pdf 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, http://mai.ru//upload/iblock/49a/w1g5yh4gjzxp3pj7dx9sgyyegvt5hgbh/08_Basharina_SHmatov_Glebov_idr..pdf 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, http://mai.ru//upload/iblock/bb5/07icz4j1yh22volz2ccnzrc3ijholmjl/09_TemnovA.N._YAnNaing.pdf 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, http://mai.ru//upload/iblock/b67/hxgz3dc77luw9cpoyff97hp53twphztw/10_Baklanovidr..pdf 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, http://mai.ru//upload/iblock/fa2/k2cfwwky2syxwuf85acf54kxfwjoq6d6/11_Vin_1_.pdf 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, http://mai.ru//upload/iblock/820/jcho8kpk2d2ma3cvxt7y37o9fxn8l144/12_Korobkov_Zaykin.pdf 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, http://mai.ru//upload/iblock/1f4/8vl68gn5a1ha6asxl77p1d5t0hssgu0x/13_Ovakimyanidr..pdf 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, http://mai.ru//upload/iblock/1f4/2p24vttv9mv2a86bl5wqk9f8ykw8g3r2/13_Gumarov_Getmantsevsutochneniem.pdf 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. 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, http://mai.ru//upload/iblock/e61/helxwofeegp1xdz0ykpfq3oo9wk52xp1/14_Borshchev_Kamyshanov_Sysoev.pdf 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, http://mai.ru//upload/iblock/602/sxse9gcz83mue6dcznyk4ova4eyhijho/15_Alievapdf.pdf 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, http://mai.ru//upload/iblock/089/nu0lrk0xhgnn00eahlhi06cocux1k1sk/17_Koshkarov_Guliy_Baryaksheva.pdf 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, http://mai.ru//upload/iblock/4b4/hhed2cvm8ub7t4mkeit51l2u6yp7f3nt/18_BUrenko.pdf 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, http://mai.ru//upload/iblock/94f/hw23wmp89ns8uv6203cgcb4t3y2u2oir/19_Mitrofanova_Zagitov_Trusov.._.pdf 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, http://mai.ru//upload/iblock/ccd/owb5m0pazwl93wz3el0fc5c0toaebumo/20_Osipovidr.pdf 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, http://mai.ru//upload/iblock/ed8/qvdkdpfmu913tnlo2f3bqk0sre0rruhi/21_Minakov_Aleksandrov_Danilyuk_Verbin.._5_.pdf 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, http://mai.ru//upload/iblock/750/myrwu68qdya54nhrj3euwcpld2dvjvv6/22_Pavlov_Gordeev.pdf 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, http://mai.ru//upload/iblock/338/y78wjsm2wy5pov71yulkfh5rndofjr0z/23_Ermakov_Evdokimenkov_Gotolev.pdf 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, http://mai.ru//upload/iblock/708/116xmjzs1iiypdecyo0k5offugf41kd5/24_Ivanenko_Egorov_Borzov..pdf 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, http://mai.ru//upload/iblock/c22/e554wany7qrj3g0dlxg04wdduv0rp7lg/25_Fetisov_Zimnikov.pdf 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, http://mai.ru//upload/iblock/cf2/ds4fdffas6pudbguvtmglf1tcl2no2xw/01_Averyanov.pdf 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, http://mai.ru//upload/iblock/f29/g0tzpupt3k77uicrz2j7c35t4usl77q5/02_Gerasimchuk_ZHiryakov_Kuznetsov_Telepnev.pdf 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, http://mai.ru//upload/iblock/b2c/310ljn2zae23i2nt8v2xs0h55lv5aiqp/03_Popov.pdf 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, http://mai.ru//upload/iblock/8cb/nx0x436l5pi1ftsyvq0wb6jenm1bjay2/04_Ledkov.pdf 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, http://mai.ru//upload/iblock/461/01cp4c83tguxl8sb9c6pc3k6ldi4nidf/05_Zuskova_Okonechnikov_Serdyuk.pdf 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, http://mai.ru//upload/iblock/4f9/ntt9y2457snnh22s4cvb1vcla11ewadt/06_Korovaytseva.pdf 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, http://mai.ru//upload/iblock/380/0u2uo2gc3y5ax4hp4f35ap9vrz9wr4in/07_Sazanov_Pismarovidr.pdf 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, http://mai.ru//upload/iblock/f57/2z5od72byt551jkw8vbympodphmn12fq/08_Dmitriev_Popova.pdf 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, http://mai.ru//upload/iblock/3ec/ymv23r2yi6wauuegktajvvd69l0x3bhi/09_Nikitchenko_Berezko_Krasavin.pdf 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, http://mai.ru//upload/iblock/e2d/msn4oex8uo68wcjb79baqefemucvz5uc/10_KHatuntseva.pdf 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, http://mai.ru//upload/iblock/fd2/8b0vug1swzzzvfa18hjkokgq564zf41v/11_Vavilov_Mustaevidr.pdf 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, http://mai.ru//upload/iblock/4b2/ee0sqwevephlgs8l7x23iqat7zt0if55/12_Babich.pdf 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, http://mai.ru//upload/iblock/889/dmcti332ny07y61d8yde65vmoz710yqt/13_Tarasov.pdf 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, http://mai.ru//upload/iblock/2dc/j2bk9x6w0q75oj42zq1min2w6hzyc0i3/14_Piganovidr.pdf 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, http://mai.ru//upload/iblock/bf7/r01dp3897qauji6oor7x121tvng4830g/15_Nenashev_Afanasevaidr.pdf 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, http://mai.ru//upload/iblock/052/uquz2d8sgiotky1czo4fgfje9vsxh5ed/16_Ispulov_Kalmykov.pdf 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, http://mai.ru//upload/iblock/aaa/ugacqgtel3tpgw6tvcig20qagjw5qyri/17_Tarasov_Milyaevidr.pdf 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, http://mai.ru//upload/iblock/09c/5lp95j54evg6xrapmin3okqsmd562jtr/18_Dyachenko.pdf 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, http://mai.ru//upload/iblock/3c6/kk9lu1lta58tbsbcmtkl3d5dtczksnf8/19_Minakov_Privalov_Bugaychenko.pdf 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, http://mai.ru//upload/iblock/f8c/0v0nygpogvew3v3d2pfi93ivdjkmlncm/20_Sentsov_Korotkov_idr.pdf 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, http://mai.ru//upload/iblock/cba/2la2tux0zxvhglurtfdf86vmte5r9uwm/21_Fetisov_Zavyalik.pdf 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, http://mai.ru//upload/iblock/62b/g2oynn4ysqc08tb08vvtxfc0u6k9kebn/22_Pavlov_Popov_Tkachenko.pdf 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, http://mai.ru//upload/iblock/d49/n42vpaagrihr77o3ai40wx362z3ep56a/23_Kasatikov_Brekhov_Nikolaeva.pdf 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, http://mai.ru//upload/iblock/432/usn1ektdfl8iwtj93405i5n8ql68efeg/24_Kuznetsova_Semenov.pdf 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, http://mai.ru//upload/iblock/1fb/nmim4mel2n0axkph9opzg3oyjjldnzwn/01_Popov.pdf 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, http://mai.ru//upload/iblock/e32/z83v1fn1e8pea33wg0etel115ng0am3c/02_Akentev_Fokina_Makarov.pdf 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, http://mai.ru//upload/iblock/31f/k0anflh01fr3jue7lumqt3urbad3y25t/03_Grishakin.pdf 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, http://mai.ru//upload/iblock/808/rc9k5y3wq3ecbyfrmtkehcpg5ctmbs8i/04_Pronina.pdf 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, http://mai.ru//upload/iblock/d8a/383y6olccn8eppjuzkau77qxnu49xwhs/05_Eremin.pdf 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, http://mai.ru//upload/iblock/f79/6l1lr0yh6tsdewu5bfipwjhaqhx9zf8s/06_Egorov.pdf 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, http://mai.ru//upload/iblock/a0e/25mws0li2ogsoob08jhwa97vqkh05o7a/07_Savin_Minkov.pdf 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, http://mai.ru//upload/iblock/a77/27y5yyfgrcg5wogx05ty04slguv3kuch/08_Baymetova.pdf 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, http://mai.ru//upload/iblock/1b6/w7g0aw4drl2s5a99ea5613kvjh1ex8ct/09_YAnNaingU.pdf 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, http://mai.ru//upload/iblock/1da/k3rek88gmaxumrwaaqbeal724vd6x2ud/10_Kanashin.pdf 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, http://mai.ru//upload/iblock/0d4/61kqzdq01n5m2bfbxxdxe4uz52wf2gfi/Vin_Temnov.pdf 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, http://mai.ru//upload/iblock/ca8/97kkg360a16b2tfxotb1am74bpdcfoar/12_Marinina.pdf 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, http://mai.ru//upload/iblock/34a/bngl86tzjh8d63p4b2iljq73wzjchntf/13_Zvonarev_Pitrin_Popov.pdf 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, http://mai.ru//upload/iblock/6a1/oarf9j5hf163q19wugi5cp2qsqw29qgk/14_Voznyuk_Kopalov.pdf 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, http://mai.ru//upload/iblock/5ec/5m9ebpmrubaqidjzbncdocxt2q9h05ml/15_Alrubei.pdf 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, http://mai.ru//upload/iblock/105/n5fdg3smbxuk90ul7m02ux9f2ca924ue/16_Baburin.pdf 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, http://mai.ru//upload/iblock/df9/tle7hhrlq083q1rs13rjyoid33evg7x6/17_Novikov_KHorchev.pdf 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, http://mai.ru//upload/iblock/9e1/f69htofiorvd6qr9en1pac4murdd5n8i/18_Olkina.pdf 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, http://mai.ru//upload/iblock/68e/yxvdf23sass5m5r0upqkes1rzsngiyom/19_Dorozhko_Musienko_Sundiev.pdf 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, http://mai.ru//upload/iblock/630/rsvxidbla802hqe3b04lm9lsmlkjlazu/20_Abdali_idr.pdf 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, http://mai.ru//upload/iblock/29b/q2hkh03pyaq4s7y910yexfun4nqndj8d/21_Nguen_Nguen_idr.pdf 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, http://mai.ru//upload/iblock/38f/3c9a1lkx0af4v1p1ptrc9k9f22e6twj2/22_Gumbatov_.pdf 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, http://mai.ru//upload/iblock/246/nzree49dnmhoe7c3a3xs2yx5x10z95j5/23_Kasatikov_Fadeeva_Brekhov.pdf 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, http://mai.ru//upload/iblock/413/1l1pmbm4gokhggybie8oflbwpffsypa0/24_Abdurashidov_idr.pdf 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, http://mai.ru//upload/iblock/040/vjgc9wkqc1i2x43ogf1ngmuppqm72v45/01_Gadzhiev_Kuleshov.pdf 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, http://mai.ru//upload/iblock/366/hhc1r5899ryn1dfmxaz8uio24d92k2lg/02_Popov.pdf 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, http://mai.ru//upload/iblock/0ad/g4nm0tghw9w9mxqffu8ync4o2cozunhl/03_Pismarov.pdf 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, http://mai.ru//upload/iblock/d98/mnlvb12e3w1r5m4jaq1i0fgoohuu7dvx/04_Balunov_Solyaev_Golubkin.pdf 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, http://mai.ru//upload/iblock/f10/kl53st35kyzzls658e1nqzmujk6aaq2k/05_Bykova_Mogilevich_idr.pdf 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, http://mai.ru//upload/iblock/cae/j4fb3qw0cz67um211g8i95pd03ebvcc5/06_Dobryshkin_idr.pdf 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, http://mai.ru//upload/iblock/b32/k8amj3zlitk90a0zvwszr3fz0hmbn41a/07_CHzho_Rabinskiy.pdf 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, http://mai.ru//upload/iblock/99b/l02v5r1qijsfrtknv59v8nodoo1yfzap/08_Tant.pdf 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, http://mai.ru//upload/iblock/4ea/cemeeeosrrrxwxekt16cygbcsotsiysl/09_CHerkasova.pdf 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, http://mai.ru//upload/iblock/b03/hk9ex7ig7hhsqcdpkxrod31p8n7esg6v/10_Kaurov.pdf 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, http://mai.ru//upload/iblock/a13/3n10pv9x30xq64jntexz5mksdvv39mx0/11_Usachev_Isaev_Sapunov_Sustin.pdf 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, http://mai.ru//upload/iblock/bf0/wz6iae5cnboq98nl0zv6c36xcn346r7q/12_Temnov_SHkapov_CHzhaokay.pdf 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, http://mai.ru//upload/iblock/acc/pgl9dhr1tg9qb71ncb1oeixt2nifl2aj/13_Biryukov.pdf 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, http://mai.ru//upload/iblock/29b/o03pipkj6rzihoih5csk125pzpnyedjd/14_Korol_Temchenko.pdf 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, http://mai.ru//upload/iblock/010/lbvbf4fvav87eip2lo67vb2w8jexc4g0/15_Alrubei_Pozdnyakov.pdf 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, http://mai.ru//upload/iblock/86b/yxpkx4tzolkymtdteajgtkb5jbc3fi4i/16_ParshutkinBuchinskiyKomlyk.pdf 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, http://mai.ru//upload/iblock/918/iv13gkvyqcan2lx43oj0rgf6p2nehnxs/17_Tyapkin.pdf 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, http://mai.ru//upload/iblock/465/51so15phqg0k62xy1b87vgvfw2g43ssl/18_Podstrigaev.pdf 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, http://mai.ru//upload/iblock/b4a/haux1t5j4vy03y0xqglqv5tqud2l7i9w/19_Sychev_Osipov.pdf 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, http://mai.ru//upload/iblock/790/texw7bdbxsa54c3regynhkqufijp5stc/20_Maksimov_Ilyushin_idr.pdf 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, http://mai.ru//upload/iblock/e0b/at2zt0d92p2ufr5k7ds6hmpa9cnpb2xr/21_Sentsov_Polyakov_Ivanov_Pomozova.pdf 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, http://mai.ru//upload/iblock/f14/59lhe9tz4e35gj698jel646en5bvm62v/22_Gumbatov.pdf 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, http://mai.ru//upload/iblock/23a/ee6elfeedmlwwnbvz9rfxl6h92e7dpg3/23_Stepanov_Pavlov_Vladimirov.pdf 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, http://mai.ru//upload/iblock/5da/ubto9wu3grsxosepn35j2hyk8c0d88fd/24_Abdali._YAkimovich_Kuvshinov_idr.pdf 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, http://mai.ru//upload/iblock/2a8/lffdsfk2mjf3ykicipscmiy79ox8omg2/25_Kuznetsov.pdf 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, http://mai.ru//upload/iblock/a96/jhsecysvja7nl8q6fpt3zcgkqg4x88jd/26_CHernikov.pdf 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, http://mai.ru//upload/iblock/5f7/1if1ss4am8i1ifcvuc2piirddt2tenb0/01_Popov.pdf _{}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, http://mai.ru//upload/iblock/f1a/relpsxh1z15houm7ox3hk154qfhjci2n/02_Kuleshov.pdf 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, http://mai.ru//upload/iblock/862/3tkrzrto0q98ggkbv8wi1fy9qaio834u/03_Borshevetskiy.pdf 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, http://mai.ru//upload/iblock/9dc/t4r2h8hprmr5941ar32vw7sljbl2cj5g/04_DobryshkinLozovskiySysoevSysoev1.pdf 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, http://mai.ru//upload/iblock/c15/0s3ko0mby638j62l0orthufwls4opfqo/05_Eliseev_Kuznetsov_Mironov.pdf 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, http://mai.ru//upload/iblock/989/pgaiofhxswge9vp1tm05fhy3hj0xcwuw/06_Temnov_YAnNaing.pdf 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, http://mai.ru//upload/iblock/2bb/v4yg2lrtspfaslnybg4p77o7zu909uc6/07_KHatuntseva.pdf 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, http://mai.ru//upload/iblock/bc7/u8bj5aq2i4c6mp94j4z0phx9j3mb2gv2/08_Kotelnikov_Kotelnikov_Krylov.pdf 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, http://mai.ru//upload/iblock/432/v81lhioi6p4wq4i7eb3656gcwr93gjo2/09_Poyarkov_Lipatova.pdf 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, http://mai.ru//upload/iblock/9d6/da46df8yd1bf3g4z4d051tn3331g50x8/10_Azarovidr.pdf 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, http://mai.ru//upload/iblock/a82/brgqpgp8ouqyamgjn2ozcbxmsns6ja8f/11_Buzhinidr.pdf 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, http://mai.ru//upload/iblock/651/7segqq76ih5mwh81zhb36m9thdwb1nv9/12_Volkov.pdf 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, http://mai.ru//upload/iblock/534/x2byk2re47dsvhp1ihqklgfw7dzyyw46/13_Tyapkin_Vazhenin.pdf 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, http://mai.ru//upload/iblock/c1b/2zl3suq2di6fp5mwbzdkz7b2fmcg0lu0/14_Korovin_Savin.pdf 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, http://mai.ru//upload/iblock/44e/eahh5vjvcq4ds21ez6nscha8qscxgbz5/Koshkarov_Semenova_1.pdf 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, http://mai.ru//upload/iblock/450/6mfhhuss3uygnfsthl52yupcqhvecbpe/16_Vataeva.pdf 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, http://mai.ru//upload/iblock/432/6ooi0mggya1vt5ayeqmvpio77kck3xf0/17_Laitidr.pdf 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, http://mai.ru//upload/iblock/c74/v7qw6olpnaivxp3zol24t3g1xwwjla8h/18_Vatutin_Klyuchnikov_Petrov_Sudar.pdf 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, http://mai.ru//upload/iblock/877/w4omg7n0i8tqaoixtou8kw91b9qkyl5z/19_Nestruev_Borzov.pdf 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, http://mai.ru//upload/iblock/ce8/ex1kqrimtx8yiyyk8tls6q6ufvx3iw2a/20_Bukiryev_Savchenko_YAtsechko.pdf 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, http://mai.ru//upload/iblock/631/totc07rtsqm46aemevte76q7fnshcxqg/21_Kabanov_Amosov.pdf 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, http://mai.ru//upload/iblock/6a4/y9y2z56d1dwwwzjc4iqclo1bd3igzzmy/22_Kopeyka_Verbin.pdf 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, http://mai.ru//upload/iblock/d59/grzao0nsc0w4r1svm2tfx4agybqs70gi/23_Knyazev.pdf 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, http://mai.ru//upload/iblock/4c7/bhkledep2uueki1aitn3xa4ju68lnrjy/01_Ledkov_Belov_Tchanikov_.pdf 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, http://mai.ru//upload/iblock/2ee/askcpt2ik8fkwfqzp9yz470ukasoil1p/02_Averyanov_.pdf 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, http://mai.ru//upload/iblock/51c/4vm3inp8f26kj59vc8w8xmsjamkh6zuq/03_Popov.pdf 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, http://mai.ru//upload/iblock/f1c/cimkmw28x135q473enpv42u5yclupxi1/04_Bogachev_Petrov_Bernikov_Sergeev.pdf 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, http://mai.ru//upload/iblock/268/ta2k4svcb21qf77mpke2tm6v0xr5kq5q/05_Kriven.pdf 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, http://mai.ru//upload/iblock/93b/qz4kt7bso7x5i3970d5ihdf4mrurqny9/06_KolodezhnovVeretennikov.pdf 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, http://mai.ru//upload/iblock/f8a/yzklywtdx3e75lhgg908h7wr5jcb32mp/07_Aleksandrov_Konstantinov_Markov_Platov.pdf 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, http://mai.ru//upload/iblock/5f2/5gi2e83n0zrsnhftgk4zpoa02jn81lnr/08_Rotermel_SHevchenko_Lizan.pdf 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, http://mai.ru//upload/iblock/a6c/4ry3k56ko7chtg6gmdvh3nc4oaxoh1eb/09_KHafadzha.Ilin.pdf 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, http://mai.ru//upload/iblock/58e/2d88k3qr30rmpd5l4s7zb8wh9uxeypmp/10_Brodskiy_Zvonarev_KHubbiev_SHerstyuk.pdf 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, http://mai.ru//upload/iblock/609/30bgr7548lcdo6nnnm6fyvj0u2abylyx/11_Dmitriev.pdf 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, http://mai.ru//upload/iblock/aac/3d9ldtbvenaokhr846o11cxl62cwq5dk/12_Abramov_YAkush.pdf 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, http://mai.ru//upload/iblock/b8e/eyle9t5xrx9yvtm0p2fbnlgki3ggxos1/13_Vakulchik.pdf 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, http://mai.ru//upload/iblock/189/35lz12x2zqfp3n4u4kkcyv3aev5m1ojf/14_Burenko.pdf 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, http://mai.ru//upload/iblock/d8e/cybhjlh8zvo40ejkhh9f5hv1pjuz47le/15_Kazantsev_Knysh_Makarov.pdf 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, http://mai.ru//upload/iblock/aca/qvzzw6vlrvv41xoc2smws8u11jvpj0ao/16_Glushkov_Moiseev_Ispulov_idr.pdf 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, http://mai.ru//upload/iblock/971/4dbrwhrmp9gjvak8dycke32ordwbsv1w/17_Aslanova.pdf 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, http://mai.ru//upload/iblock/968/eaol24mcpszrzegg5d6m55toonga6kia/18_Gorbunov_Nenashev_Mazhitov_KHadur.pdf 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, http://mai.ru//upload/iblock/d97/m5ht0m80ouorsof4ca4dmj8lz9x8kimn/19_Vernigora_Kazmerchuk_Sysoev.pdf 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, http://mai.ru//upload/iblock/210/knje6w7b4y80y00lruneq69zqnant39h/20_Dzhavadov_Agaev_Guseynov_Zulfugarly.pdf 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, http://mai.ru//upload/iblock/b63/4cub5wida789zh9pmogd0pw177fc0c2a/21_Maletin_Glushchenko_Mishina.pdf 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, http://mai.ru//upload/iblock/068/bek6nsduu39vrjetil9j0nmrc5trylts/23_Travin_Kalashnikov_Bakradze.pdf 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, http://mai.ru//upload/iblock/696/9ern1kdeofh6cvsu7b8kzoxii3sent7a/24_Lazeev_Litovka.pdf 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, http://mai.ru//upload/iblock/542/cr54u58xf7udombk779x0iuf5eo04zqt/25_Molotkov_Tretyakova.pdf 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, http://mai.ru//upload/iblock/e7e/0t53bs4yusjmvvmru9k3olnybn41ab42/22_Vatutin_Klyuchnikov.pdf 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, http://mai.ru//upload/iblock/90f/ln9lqg8yjeudn6suvgzp114p0yjk0sxr/01_Popov.pdf 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, http://mai.ru//upload/iblock/cca/xgst10tkbjwg0v6qthn69gszhiekyax3/02_Safonov.pdf 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, http://mai.ru//upload/iblock/11f/iwgpqzr98pggy1xj6gr55gzcplgl93xk/03_Avdyushkin.pdf 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, http://mai.ru//upload/iblock/79b/kt66qs88lka6rx9cjet5l5v4kayrusvy/04_Martirosov_KHomchenko_1..pdf 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, http://mai.ru//upload/iblock/7d6/hmeacnm5rtbnl4lhlt1pmbuvwv6y31y1/05_YUyCHzhaokay_Temnov.pdf 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, http://mai.ru//upload/iblock/177/vm9x9626jhtabrunqa68u63u8iff73m5/06_Kutysh.pdf 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, http://mai.ru//upload/iblock/228/51fvojiwvv2o2ws7uwovwbmyvg4c2btg/07_Averyanov_Zinin.pdf 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, http://mai.ru//upload/iblock/70f/thuaux5awqva6opwqe4e6hi0pdvoj5vi/08_Lebedev_Repin.pdf 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, http://mai.ru//upload/iblock/0d5/c7i7uijczoof0uu43faapi835tari1on/09_Goncharov_Kopeyka_Babin.pdf 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, http://mai.ru//upload/iblock/0a6/xvvfnj11z4r1bvl1ae0f065pljltojkl/10_SHA_idr2_.pdf 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, http://mai.ru//upload/iblock/02f/z2ilh6xiyd5zu4r4qgl23vv3lqf1w54w/11_Sedelnikov_Orlov_Serdakova_Nikolaeva.pdf 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, http://mai.ru//upload/iblock/88e/4zv7zp14kg6ia1ga21aterm6ne8pxc2q/12_Polyakov_SHesterkin.pdf 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, http://mai.ru//upload/iblock/ba6/nu24tkqnm105g3colnic618q7opi8597/13_Dinyaeva_Kravtsov_Krumlyakov_Benkalyuk.pdf 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. 
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