2017. № 97
Mechanics  
Theoretical mechanics  
Space debris active transportation employing a space tug with a tether link is one of the promising techniques of nearEarth space cleaningup. When developing such transportation means, it is necessary to account for the specifics of space debris objects, particularly, the presence of elastic structure elements, and fuel remnants. There are two types of the space debris, namely, overaged spacecraft and orbital stages of rocket carriers. On one hand, orbital stages are simpler for transportation compared to spacecraft, since they do not contain large attached elastic elements, such as antennas or solar batteries. On the other hand, orbital stages might contain fuel remnants affecting the motion of space debris and the transportation system at large. The presented work is devoted to this phenomenon. The purpose of this work is development of a simple mathematical model of a transportation system with account for the fuel remnants onboard the space debris object of a space station type.
The article studies the effect of fuel remnants on the safety of withdrawal the space debris with fuel remnants. The authors obtained equations of motion in central gravitational field of a mechanical system, consisting of a space tug, space debris object and a tether. The space debris object is considered as solid body, containing a moving mass of liquid. The liquid fluctuating in the tank is represented as an equivalent pendulum system. Stationary solutions of the equations of movement were found, and linearized equations in the neighborhood of stable stationary solutions were constructed. The results of numerical modeling, demonstrating the closeness of analytical solutions of the linearized equations and numerical solutions of the initial equations of motion are presented.
The obtained linearized equations can be useful for determining transportation system parameters, ensuring safe withdrawal of the space debris. Keywords: space debris, tether, space tug, cavity with fuel, oscillations 

Deformable body mechanics  
Rheological effects such as creep and relaxation may appear in the material when operating under longtime load. This can lead to a delayed fracture, so it is important to analyze the regularities of polymer composite materials deformation with account to the time factor. The presented article considers models implemented for describing rheological effects, shows their advantages and disadvantages.
The most common cases of loading can be described by the relationships of hereditary mechanics. Besides the fact that the hereditary approach is the most common form of a relationships between stresses and deformations at time varying loads, it allows identify a number of interrelated functions characterizing the material.
A model based on the matrix equations of the theory of laminated plates and relations of a hereditary type is proposed. It allows establish the dependence of deformations from time under timevarying loading.
To reveal time effects, the test for creep and relaxation of BMI3/3692 carbon fiberreinforced plastics samples with reinforcement scheme [±45°] and KMU4L with reinforcement scheme [±20°] were performed. The BMI3/3692 samples were tested for creep at timevarying loading also. The KMU4L samples were tested for creep and relaxation. Resistive strain gages were employed to register longitudinal and transverse deformations. Nonlinearity and hysteresis are appearing on the stressstrain diagrams of the tested samples. Likewise, the diagrams of stresses and deformations are essentially dissimilar to each other, which can be explained by timedependent factors.
Calculation for BMI3/3692 carbon plastics with reinforcement scheme [± 45°] and KMU4L with reinforcement scheme [± 20°] was performed employing the model proposed in the work. The Abel kernel was chosen as a creep kernel. Rabotnov kernel was used as a relaxation kernel.
Mechanical characteristics of the BMI3/3692 carbon plastic were determined: E_{1} = 84 GPa, E_{2} = 80 GPa, ν_{12} = 0.04. G_{12} = 7.5 GPa. . The kernel parameters were determined by the leastsquares method. Minimum of disparity of computed and experimental parameters was determined numerically. The following parameters values were obtained: α = –0.7, β = –0.05, k = 800.
The elastic characteristics of the of KMU4 carbon plastic monolayer were determined: E_{1} = 150 GPa, E_{2} = 4 GPa, ν_{12} = 0.32. G_{12} = 3.3 GPa. The kernel parameters were also determined numerically: α = –0.8, β = –0.05, k = 150.
The article presents the graphs demonstrating a good correspondence between calculated and experimental data.
The proposed model can be used to calculate the stressstrain state of composite structures while longterm deformation. Keywords: carbon fiberreinforced plastic, hereditary mechanics, creep, recovery, theory of laminated plates 

Fluid, gas and plasma mechanics  
Gas ejector is a convenient device for verifying mathematical models, which is based on comparison with experimental results. Advantages of flow in an ejector for a numerical experiment:
The authors considered a singlestage axisymmetric ejector of the classical singlenozzle design. Compressed nitrogen was employed from the balloon system with a stagnation temperature of 300 K. The article presents all necessary geometry, inlet pressure in the ejection nozzle, and the pressure sensor positions. The sensors scanning slot is 0.001 s.
Data collection system ensured the time interval of 0,001 s between the two sensor readings. The sensors error was less than 35 Pa (0.005 psi). The results of various launches were not being averaged.
Onedimensional theory comparison with the experimental data reveals that the 1D theory gives a lower (optimistic) estimation of the startup pressure. The experiments demonstrated also that minimum level of the ejector highfrequency noise corresponds to the minimum stable pressure in the vacuum chamber.
A numerical simulation of the ejector operation for several variants of the ejecting gas pressure employing the authors’ original code based on I.Kryukov and I.Ivanov code and Godunov’s method was carried out. The vacuum chamber pressure fluctuation and the shocktrain separation point displacement were obtained. A numerical experiment yields acceptable average flow parameters, but absolutely unacceptable frequency characteristics.
The presented experimental data are quite complete and suitable for turbulence model verification.
The work was supported by the RFBR grants No. 163860185, No. 160100444a.
Keywords: gas ejector, vacuum pump, experimental data, gas jet, shocktrain, separation point boundary layer, numerical simulation, Godunov's method 

Aeronautical and SpaceRocket Engineering  
Aerodynamics and heatexchange processes in flying vehicles  
Keywords: aerodynamic forces and moments, angular velocity components, rotary derivatives 

Design, construction and manufacturing of flying vehicles  
The article considers specifics of modeling the phenomena of the dynamic aeroelasticity, such as flutter and bugging, on dynamically congruent models in the wind tunnels (WT) in transonic range of Mach numbers.
The goal of the research is developing recommendations on similarity criteria selection for modeling the phenomena of aeroelasticity in the transonic mode by additive technologies.
The major stages of this work are analysis of existing structures of transonic aeroelastic models by weight, stiffness and strength characteristics, and comparative analysis of model materials’ specific stiffness and strength characteristics.
The article gives recommendations for the similarity criteria selection while design, manufacture and testing of dynamically similar models (DSM) in transonic WT. Implementation of the synthesized criterions will allow obtaining the reliable results of the experiment and successful transferring to the fullscale design.
It was shown, that the major problem is caused by the fulfillment of the mass similarity condition – the Newton’s criterion. This problem is stipulated by models’ structure overweighting. The article gives examples of overweighting effect on the flutter critical speed.
The design features of the main types of transonic DSMs force diagrams were considered. The effect of the main strain load carrying elements’ cross sections shapes of DSMs on DSM’s weight effectiveness was considered as well.
A comparative analysis of the specific stiffness and strength characteristics of homogeneous materials (metals), thermoplastics and isotropic composite materials was performed. This analysis results allowed obtain estimations of weight efficiency when used in DSM designs.
The article presents also the prospective directions for weight reduction of models of beam and plate scheme. Keywords: aeroelasticity, dynamically scaled model, additive technology, similarity criteria, aerodynamic experiment, composite materials 

Strength and thermal conditions of flying vehicles  
This paper covers the slip ring assembly layer total resistance estimation method. This method is meant for application upon slip ring assembly design and engineering. The primary objective of this paper was to obtain the capability of slip ring layer heat dissipation simulation modelling based on the equivalent circuit.
The role of the slip ring assembly in the spacecraft electric power subsystem is considered; the basic structural elements of the assembly are described; the principles of operation of the device are explained. The major output performances of the slip ring assembly such as the voltage drop value across the layer of the slip rings and the total power dissipated on the device are defined. The process of current flow through the slip ring assembly is demonstrated. An equivalent circuit for a layer of slip ring assembly with ten contact rings is presented and reviewed in detail. The equation system for the equivalent circuit loop currents is defined. A relationship between the contact resistance and the impedance of the slip ring layer is established. Contact resistances are introduced into the system of equations. The formula of the impedance function of the layer of slip rings layer is obtained from the value of the contact resistances. The total resistance and the heat dissipation value of the slip ring layer upon nominal slip ring installation are estimated. The experimental and theoretical plots of the slip ring assembly layer impedance variation are provided for comparison. The adequacy of the assumptions taken and acceptability of the technique for practical application was validated. The analysis of contact resistance variation value versus the slip ring layer total resistance in case when the inner ring is displace versus the outer one was carried out.
The paper concludes that there is satisfactory convergence (within 4.5%) of the theoretical results with experimental data. Application of the above technique will allow predicting the slip rings heat dissipation variation during the design phase as well as to estimate their lifetime with lower costs. Keywords: power supply system, currentcollecting device, ring, transient resistance, equivalent circuit 

Thermal engines, electric propulsion and power plants for flying vehicles  
Currently, the engineering practice widely uses software packages for engineering design automation. They include the systems allowing solve complex problems of computational hydrogas dynamics. The specificity of the employed mathematical tools imposes certain constraints in the course of operation. Thus, there is no universal mathematical model at present, which would reliably describe all turbulent flows specifics for the entire spectrum of problems. Instead, there are many semiempirical models correlating well with the experimental data for only a certain range of problems.
The most widely used models are the models of Reynolds averaged Navier–Stokes equations. At the same time, these models have a greater number of variations, most of which found application in commercial software packages as well. Such diversity creates the problem of selection of the most appropriate model for the particular solution case. Thus, verification and validation are the intrinsic part of the turbulent flows numerical modeling.
The purpose of the article is the methodology of verification and validation of a flow computing in a combustion chamber airgas channel of a gas turbine engine with transverse vortex system. The authors performed reviewed the most relevant turbulence models employed in software packages of computational hydrogas dynamics. Their advantages, disadvantages and constraints associated with the empirical data are listed.
Based on the developed combustion chamber model, the fullscale model for hydrodynamic research and the finite element mesh for calculations in the software environment were created.
The article presents the results of experimental studies and the results obtained by numerical methods. They performed their comparison and analysis. Based on this data, the two models corresponding to the selected confidence interval, were separated out.
At the next stage validation of turbulence models was being performed. As a result, it allowed give qualitative estimate of flow kinetics over the entire computation region.
Verification revealed that of all the models considered, the best conformity with experiments was ensured by the SST kw model and standard ke model.
In consequence of validation, the authors managed to find that the SST kw model reproduced the flow kinetics in airgas channel of the combustion chamber with a transverse vortex system more correctly. Keywords: verification, validation, computational fluid dynamics, turbulence models, combustion chamber, gasturbine engine 

The subject of this work is the power unit of the space nuclear power plant in the test bed version. The purpose of the work was to develop a general methodology for calculating the power unit of the test bed version of a nuclear power plant for space applications in transient operation modes. An additional task was to determine the minimum set of independent variables, allowing fully characterize the operation of the power plant in nonstationary modes.
The computation technique is based on a unifying physical and mathematical model of the power unit. The physicomathematical model is being built on a modular principle and includes the models of all the components of the power unit along the energy conversion contour. The article describes also the algorithm and the scheme for calculating the parameters of a closed gasturbine circuit in a nonstationary formulation. The technique and algorithms are described on the example of a test bed version of a space nuclear power installation with a resistor heater as a heat source.
This technique can be used to perform calculations while the design, development and evaluation of space nuclear power units efficiency, as well as in modeling and developing control algorithms for the energy conversion loop in the modes of the source thermal power alteration. The technique can also be changed and supplemented depending on the layout and design of the particular power unit, the characteristics and specifics of its constituent parts, the type of heat exchangers, heat source, etc.
The main feature of the work is that this technique allows compute all most important parameters of the energy conversion circuit of a space nuclear power unit exactly at nonstationary operating modes. This is necessary at the startup phase and while switching from one mode to another for development of control algorithms for the entire spacecraft. Keywords: mathematical modeling, gasturbine loop, Brayton cycle, space nuclear power plant 

Dynamics, ballistics, movement control of flying vehicles  
Methodology for aircraft rational control law forming while performing maneuvers in horizontal plane
The article presents the methodology for agile aircraft rational controls forming while executing a turn in horizontal plane. The flight of an agile light airplane is selected as an object of study. While solving the problem of rational trajectories selection provisions of the direct variation method were assumed as a basis. The existing techniques, where the reference trajectory is set as dependence of phase coordinates from the physical time in the form of a polynomial, exhibit a significant drawback. This dependence of an aircraft speed from the trajectory geometry, i. e. time derivatives of coordinates, uniquely determine the speed at each point of the trajectory. A distinctive feature of the proposed methodology from the existing one is the aircraft control laws forming method. Control functions for aircraft roll and normal speed overload herewith are determined from the required accelerations for monitoring reference trajectory, specified in the form of polynomial dependence of phase coordinates from time. Tangenital overload control is formed on the assumption of specifics of maneuvering in horizontal plane. These features consist in the existence of a certain flight speed, at which maneuvering in horizontal plane is performed with maximum angular rate of turn. The degree of approaching this rate herewith is determined by the moment of the engine operation mode switching, and ensures the possibility of fuller realization of aircraft performance characteristics inherent to its structure (maneuvering characteristics).
Thus, the developed methodology ensures the accounting for maneuvering specifics in horizontal plane while forming an aircraft speed mode control, and allows eliminate the “stiff” dependence of flight speed from the trajectory geometry. It allows also determine the rational trajectory of the combat maneuvering in the horizontal plane, by which high levels of maneuverability inherent to the aircraft structure are achieved.
Application of this methodology is possible while developing the systems of intellectual support for a pilot’s decisionmaking, as well as aircraft automatic control systems. Keywords: aircraft, flight dynamics, control law, maneuvering in the horizontal plane 

Instrument making, metrology, information and measuring equipment and systems  
Navigation instruments  
Computer aided design systems have been widely used in developing of various technical systems. Concern CSRI Elektropribor has a long experience employing PTC Creo Elements, which shows an effectiveness of 3D modeling employed in innovative navigation devices. It allows both increasу labor productivity and cut devices developing time by paralleling activities while working on project. Moreover, it ensures quality improvement of the systems under development, while 3D models are working well for both finite element analysis of mechanical characteristics and rapid prototyping. Thus, 3D modeling has become a design standard for gyroscopes being the most complicated navigation instruments.
At present, a hightech manufacturing faces such a critical task as developing innovative and competitiveness products. That is why risky and challenging solutions should be applied for navigation devices design. Correctness of these solutions could be achieved in two ways: computing and prototyping. As the first way, finite element analysis is widely used around the world as nonalternating method of predictive modeling. In recent years, with advancement of additive technology, devices prototyping and, sometimes, their manufacturing is being provided by 3D printing. Highlighted sequence of design provides a systemic approach to the developing based on uptodate technology and allows suggest the following method of navigation devices design. 1) Developing 3D models of devices’ parts and assemblies. 2) Employing finite element analysis of devices’ mechanical characteristics. 3) Rapid prototyping by additive technology. 4) Errors’ determining and correcting.
The method differs from the others by implementation of closed process “design, modeling, manufacture”, which provides improvement of products quality and labor productivity. Moreover, this method is recommended for bachelor students teaching on design basics. It contributes essential part in developing engineer skills of students . Keywords: 3D modeling, FEM analysis, rapid prototyping, additive technology, CAD systems 

Information and measuring and control systems  
The basis of technical support for information, measurement and control systems consists of electronic devices and systems for communicating, gathering, processing, transmission and display of information, which, in stages of development and production, are subjects to diagnosis.
For means of checkup and most of other types of control system tests, it is common to use checkout equipment (CE). The CE hardware and software are developed individually for the needs of specific tests of inertial control system. To simplify the design and improve versatility, this article offers to rethink the software design methodology for CE, allowing forming CE software automatically for control and diagnostics purposes of several similar inertial control systems. This solution will significantly reduce the time and cost of developing hardware and software parts of the CE.
Forming of the software is performed by attaching additional software modules (ASM), which are responsible for unique to a particular inertial control system (ICS) equipment or functionality, to basic software module (BSM). Designed software remains unchanged while being used for control and diagnosis of various ICS’s. BSM performs such functions as distributing software threads and their priorities, ASM launching and control. ASM are developed in conjunction with CE and have unique features. Interaction between the modules is performed by means of shared memory and communication protocols between modules. To sel ect ASM’s necessary to complete the specific test job, the software should analyze digital data, incoming fr om the control system. This dataanalyzing algorithm is separated into several major steps: searching for keywords employing reference list, comparing reference lists and detection of ‘answer’ keywords. Keywords: checkout equipment, modular system, software, inertial control system, control and diagnosis 

The authors consider the problem of information processing in measuring information systems of unmanned aerial vehicles’ (UAV) at lowfrequency interference. As a rule, the classical approach to solution of the problem of lowfrequency interference filtering proves to be unusable due to the estimates divergence. The authors propose to solve the put forward problem by employing optimal filters realizing the «interference whitening». The thus obtained mixture of valid signal with white noise The suggested algorithm of optimum filtering consists in preliminary passingthrough of a measuring instrument output signal through the forming wideband filter. The thus obtained mixture of a valid signal with white noise is fed to lowfrequency filter forming an optimum valid signal estimation. The structure and parameters of the synthesized filter depend on the nature of the lowfrequency interference in the measurement channel. As a rule, intensity of UAV’s trajectory fluctuations can be considered as approximate constant and not depending on UAV control system type. On the contrary, dispersion of noise disturbance, may either increase, or decrease while UAV approaching an object. The nature of the organized interference depends on jammer actions. The optimum filtration algorithm has been constructed for both cases. The disadvantage of the proposed approach is the unjustified complexity of optimal algorithms implementation for solving applied problems. The main problem consists in an adequacy of the developed mathematical model (linearity, a small order of the equations, unauthenticity of basic data and other) to the real system under study. It feels particularly sharp while creating the UAV navigation and guidance algorithms with their tight restrictions on speed and memory of the onboard computer. One of the effective ways to solve this problem is to replace the differential equations for the coefficients that determine the passband of the optimal filter by their steady values, calculated by algebraic formulas obtained from differential equations. The simulation obtained results allow draw conclusions on the applicability of the proposed approach to filtration problems in the optoelectronic and radio engineering measuring information systems of UAV. In this case, the accuracy of angular coordinates estimating of the object of observation will decrease by 10–15% of the true values. Keywords: measuringinformation system, information recognition and estimation, lowfrequency interference, white noise, optimal filtration 

Radio engineering and communication  
Radio engineering, including TV systems and devices  
There is a need for standard time signals and frequencies in various spheres of action. The necessity for frequency and time synchronization of technological and information processes at spacecraft (SC) groundbased automated control complex (GACC) is of special topicality. The article presents the main central timing system (CTS) modernization for SC GACC as well as specifics and perspectives of SC CTS GACC while employing data transmission channels of satellite communication system (SCS) “Primorka” and satellite radio navigational system (SRNS) GLONASS. The object of the study is SC CTS GACC. The subject of the study are methods and means of time signals distribution. The purpose of the study consists in increasing SC CTS GACC stability by implementation of data transmission channels of the SCS “Primorka” and the satellite radio navigational GLONASS system (SRNS). System analysis of methods and means of time signals propagation in SC CTS GACC, and possible synchronization error sources was performed in this work. The block diagram of SC CTS GACC creation with threelevel architecture was developed. The upper level (the CTS backbone network) is between the State time references and central stations, which will meet the strict requirement on characteristics quality. The intermediate level between CTS central points and CTS peripheral stations will be connected by SCS “Pimorka”. The low level – between CTS peripheral station and a customer SC GAACC, accounting for the SC GAACC requiremetns. Realization of the proposed threelevel SC CTS GACC will allow significantly increase the SC CTS GACC stability. Keywords: central timing system, automated groundbased control system, satellite communication system, satellite radio navigational system, synchronization 

The paper introduces cyclic periodogram averaging block algorithm for the estimation of cyclic power spectral density (CPSD) using timesmoothing approach. A brief overview of the cyclostationarity phenomena and the corresponding cyclic characteristic functions are provided; a detailed theoretical description of the proposed algorithm focusing on the task of cyclic power spectral density estimation of the finite length digital infocommunication signals is presented. The structure of the CPSD function on bispectral plane for the case of finite length digital signals is described. The properties of the support region of CPSD on bispectral plane such as resolution element shape and effective width are taken into the consideration in order to avoid significant gaps alongside cyclic frequency axis.
In order to demonstrate the proposed algorithm as well as the advantages of the cyclostationary approach itself, a numerical simulation is carried out. A mixture of two amplitudemodulated signals with widesense stationary random processes used as their modulation sequences is chosen for the simulation. The parameters of the simulation such as effective bandwidths of the mixture components and their carrying frequencies are selected in a manner that a significant overlapping in the frequency domain is to occur. The analysis of the estimated cyclic power spectral density as a twovariable function obtained with the proposed algorithm allowed to successfully determine the number of the components in the signal mixture, their carrier frequencies, separated periodograms for each of the components and make the conclusion of the statistical independency of the underlying random processes. The results of the numerical simulation confirm the correct work of the proposed algorithm as well as demonstrate the selective properties of the cyclostationary approach.
Keywords: cyclostationarity, cyclic spectral power density, nonparametric estimation methods, periodograms, spectral correlation analysis 

Antennas, SHFdevices and technologies  
Design of ground mobile communication systems operating in urban conditions, including episodic networks, requires accounting for the effects of various factors of radio waves propagation on the received signal parameters. Depending on the types and urban building density the signal may contain include lineofsight, reflected, diffracted and refracted components [1]. In the absence of a priori knowledge of obstacles’ type, size and shape the path loss can be estimated based on measurements. Empirical estimation should bear statistical character and based on determination of median values of path loss.
Due to the terrain and building types variety as well as the relative position of transceivers and, hence, difficulty to predict the effect of particular factors along the propagation pass on radio waves damping, a universal model for losses calculation while radio waves propagation in urban conditions does not exist. Models for predicting the signal level in ground mobile radio communications system can be employed only in cases of mobile networks with highly raised antennas of basic stations. Due to the growing popularity of the urban wireless networks (WLAN) and mobile ad hock networks, implicating a large number of mobile transponders, the purpose of this study is predicting of radio waves propagation at lowlying antennae in urban conditions by modifying the existing models on the ground of experimental data.
Based on the experimental study at the frequency of 870 MHz performed in Zelenograd, radio waves propagation losses were determined in conditions of urban building. The obtained experimental values of propagation loss were applied for linear approximation. The values of coefficients were determined and Stanford University Interim (SUI) model modification was suggested for urban media for the cases of antenna suspension height of up to 10 m. The article demonstrates that while estimating radio signal propagation in urban conditions with lowlying receiver antennae the attenuation degree equal to four can be employed. Keywords: radio wave propagation, propagation in urban area, empirical models, propagation loss 

The paper considers one of the problems occurring in microstrip antenna arrays, namely the effect of “blindning” when the array radiation vanishes at certain scanning angles. The topicality of this problem is associated with wide implementation of antenna arrays in various Earth exploration satellite systems including synthetic aperture radars.
Fr om the published sources we know that this is due to the interaction of surface waves supported by the structure of the antenna array, in this case a dielectric layer, with dominant Floquet mode. Determining angles whereby the risk of “blinding” occurs is possible by applying the plane of phase constants, wh ere both Floquet modes and surface waves, excited in dielectric substrate of the microstrip antennae array, are depicted. The intersection of the circles corresponding to the surface waves with the circle of the radiating Floquet mode at a given scanning angle will mean the possibility of “blinding”.
This method was applied to the two dipole microstrip antenna arrays: in the first case the dielectric of the substrate was selected in such a way that only one surface wave of electric type was excited. In the second case, three surface waves were excited − two of electric type and one of magnetic.
Possible “blinding” angles were determined by performing plotting on the plane of phase constants. They were verified hereafter by modeling of an infinite antenna array, which allowed obtaining radiation element diagram. All the “blinding” angles found analytically appeared on the radiation patterns. The angle, not appeared while simulation, took place only in the second case, which corresponds to the theory, since the appearance of blind angles can depend, for example, on the method of the radiator excitation. The method applicability for the considered problem was confirmed thereby.
The conditions ensuring the absence of blinding angles at a given range of scanning angles were formulated hereafter. The restrictions are imposed herewith on both the distances between the radiating elements and parameters of the dielectric substrate. A famly of curves representing the dependence of maximum distance between radiating elements from maximum scanning angle of microstrip antenna array was plotted. It allowed determine structural parameters of antenna array by the maximum value of the scanning angle. Keywords: microstrip antenna arrays, surface waves, scanning, Floquet modes, radiation pattern 

Systems, networks and telecommunication devices  
With account for the trends of mobile selforganizing communications networks development, the number of technologies and communication systems employing the principle of infrastructure building without the use base station will increase in subsequent years. Thus, more and more tasks, which should be solved on a data link layer of the system developed, are being revealed. A base station absence in the network topology generates the tasks of organizing the message delivery route selecting, which is especially important in mobile selforganizing communications networks. The concept of mobility itself, i. e. nodes’ permanent spatial motion imposes additional restrictions on the communication system. Thus, the problem of transmitting the service and information frames in conditions of a nonconstant connection between nodes occurs. Currently, one of the most widely used algorithms for the environment accessing is the CSMA\CA algorithm. Stations and subscribers of the 802.11 network, that is, WiFi networks are operating on its base. The algorithm is based on the principle of transferring the service frames of the RTSCTSDATAACK format. Using this algorithm allows solving the problems of a hidden node. The MACA algorithm lies at the heart of the implementation of CSMA\CA and is distinguished by the use of RTSCTSDATA service frames, without delivery confirmation. These algorithms have disadvantages, such as a large number of service frames in the communication channel and a possible nondelivery of the service frame with a changing network topology.
To solve these problems, an algorithm MMAC was developed. Application of this algorithm implies the presence of two or more communication channels by each node: separate communication channels for the transmission of service frames and for the transmission of data frames. Since this imposes additional costs on the implementation of the second channel, the algorithm has been modified. The LCM MAC algorithm employs the principle of separate transmission of service and information frames in different time slots.
A study of their efficiency was performed by simulating these algorithms in the software environment of Network Simulator 3. Analysis of simulation results revealed that the access algorithms for the MMAC and LCM MAC algorithms demonstrate the best packet delivery rate and network bandwidth compared to the MOCA and CSMA\CA algorithms (at the average by 20% and 500 bit / s, respectively). Based on the performed work, it was revealed that the actual task of research and development of a mobile selforganizing communication system, namely its data link layer, is the solution of a number of tasks:
Keywords: MAC, access algorithm, AdHoc 

Radiolocation and radio navigation  
The article describes the model of spaced radar system with uncooperative radiation sources, integrated into a set of national technical means of spacerocket machinery tests monitoring. A model based on estimation of spatial and accuracy characteristics of complex ballistic targets elements allows selecting a rational variant of implementing a set of national technical means of monitoring at the finish area of foreign missile testing grounds.
In general terms, a mathematical model of a simulationanalytical type of a spaced radar system is being represented in a form of an interrelated structure and includes models of uncooperative source of illumination, complex ballistic target and receiving site integrated to a set of national technical means of control. Potential accuracy of coordinates measuring of a complex ballistic target was computed. Сriterion of optimality was selected as an arithmetic mean of range estimation CSR. The required information zone is represented in the form of a discrete set, for which maximum possible number of the receiving site allocation variants was determined. Further, applying the directsearching method the value of the target function is determined for each variant of the set, which meets the specified limitations. Then the variant ensuring the goal function minimum is selected. Selection of the receiving site allocation rational variant allows realize potential capabilities of the spaced radar system for complex ballistic targets detection and measuring its’ coordinates in the full.
The proposed model of spaced radar system with uncooperative radiation sources integrated into a set of national technical means of monitoring spacerocket machinery tests being carried out by foreign countries allows select rational location and direction for receiving site at the finish area of foreign missile testing grounds. Keywords: spaced radar system, uncooperative source of illumination, national technical control means 

At present, algorithms for coordinates and parameters evaluation of the air target (AT) movement on fighters are realized based on simplified filtering algorithms, particularly by α,βfiltering and α,β,γfiltering. The main drawbacks of these algorithms are insufficiently accurate and stable tracking of maneuvering AT while low rate of information update and missing of adaptation to rapidly changing air combat (AC) conditions. Implementing of more complex models of a relative movement of a fighter and AT with refined parameters is one of the possible ways to overcome these shortcomings. The purpose of the paper is a comparative assessment of the filtration accuracy when tracking a maneuvering AT in angular coordinates using the α,βfiltering algorithms and the Kalman filter (KF) for the Zinger and Song models with refined parameters at a low rate of data update about the target. In the interests of obtaining an extrapolated evaluation and the operation of filtering algorithms, determination of the values of the maneuverability coefficient when an AT is performing the combat turn is required. The data on the AT spatial movement was obtained by semidetailed simulation on the flight testbench. Maneuverability coefficient determination was performed via correlationspectral processing, by a transition from the time domain to the spectral domain – the direct Fourier transform. To achieve the purpose of the work, modeling of the filtering algorithms at a low information update rate about the target has been performed by statistical tests method. The mean square deviation of filtering errors has been used as an accuracy index. The α,βfiltering algorithm for the model of uniform rectilinear motion, the KF algorithm for the Zinger model, and the KF algorithm for the Song model have been analyzed. Analysis of the presented results allows us to draw the following conclusions:
Thus, to ensure high tracking accuracy of the maneuvering AT in angular coordinates in the AC conditions at a low information update rate in modern aviation sighting systems, it is advisable to apply filters that employ models of relative target movement of higher orders. The filtration accuracy index increase for the KF with the Song model is 40%, as compared to the α,βfilter, and 30% for the KF with the Zinger model. However, if AT maneuver changes, it will be necessary to implement the procedures for adapting the filter parameters to the maneuver type. In addition, the filtering algorithm selection should be performed either by the criterion of the estimation error minimum or by the criterion of the transients minimum time. Keywords: maneuvering air target, Zinger model, Song model, maneuverability coefficient, combat turn, mean square deviation 

Informatics, computation engineering and management  
Mathematical support and software for computers, complexes and networks  
The following work is focused on the topic of enhancing the reliability of distributed services using container virtualization technology. An infrastructure based on container virtualization is presented and analyzed in the environment of changing workloads. Means of deployment, monitoring and lifecycle management are included in the infrastructure. The solution also includes a thorough description of networking exchange between services and servicemonitoring system interchange of data in a multitenant environment. In modern datacenters the efficiency of resources usage is based on the number of business applications per host unit, while maintaining the isolation of applications from each other, as well as providing the stability, backup and disaster recovery, lifecycle management and network interconnections control.
The article compares the benefits of full and container virtualization, as well as analysis of serviceoriented architecture on the base of container virtualization. The instruments analyzed from full virtualization perspective are VMware ESXi, KVM, Microsoft HyperV, Citrix XenServer, while OpenVZ and LXC/Docker technologies were reviewed from the side of container virtualization. One of the most important criteria analyzed is the scalability of the resulting solution built using the virtualization instruments presented above. Using container virtual machines, the number of objects on each host greatly grows, which is a more effective usage of resources from one hand, but poses a problem of monitoring and lifecycle management of a much larger number of objects on the other hand. The article analyses the network infrastructure and the monitoring toolset designed to handle much larger numbers of controlled objects than what is currently available on the market.
A hybrid architecture of Token Ring and Partial Mesh domains are presented as the more scalable and effective solution in the article for network communications between container hosts and between containers themselves. This hybrid approach is also applicable in different infrastructures build for high loads and big data processing. Keywords: container virtualization, system faulttolerance, hypervisor, distributed networking 

Mathematica modeling, numerical technique and program complexes  
The article proposes the diagram of computeraided exploratory testing of calculation and control of the flight task software developed by State Rocket Centre “Academician V.P. Makeyev Design Bureau”. Calculation and control of the flight task software (ССFT software) is a key system of rocket complex and prepares for intercontinental ballistic missile’s flightcontrol system data, special automatics, and flightcontrol system of detachable elements. ССFT software consists of programming modules developed by engineers of State Rocket Centre and related organizations. Programming module (PM) is a functionally completed software implementation of CCFT particular task (algorithm).
To ensure quality and reliability every programming module should be debugged and tested in autonomous operation. Reliability of programming module is the probability the module operation without crash.
In this work the author suggests applying a method of computeraided exploratory testing for debugging and testing PM from CCFT software. This method accounts for input parameters’ priority built on the basis of computational stability index of explored tasks.
The testing diagram accounts for programming modules’ potential crash. It is based on determination of input parameters’ priority. The author suggests employing priorities that are based on computational stability of tasks.
The testing diagram can specify the test data area variation and makes the best use of testing time resources. The diagram also performs qualitative evaluation of calculation and control of the flight task software’s functionality. This diagram is being used for CCFT software testing by engineers of State Rocket Centre. Keywords: flight task calculation and control, exploratory testing, data priority, computational stability 

The paper considers one of the possible approaches to solving the problem of linear dynamical systems control and diagnostics. Analysis of available publications [2, 4, 9] on the subject revealed that the statement of the problem of diagnostics assumes knowing of the current values of the dynamic systems state vector. However, measuring all the state vector coordinates is not always possible. Firstly, such situation may arise due to the lack of “access points”. Secondly, if the measurement results of some of the state vector coordinates contain “unacceptable” errors, which do not allow them to be used to solve problems of control and diagnostics of objects.
The proposed approach presupposes the existence of a control points shortage, but requires the observance of Kalman’s observability conditions, which allows restoring all the coordinates of the state vector. With this regard, the problem posed combines three problems: the problem of estimating the coordinates of the state vector, the problem of determining the altered parameters of the object, and the problem of determining the moments of appearance of these alterations (the moments of “discord”). Solution of the first problem is traditionally associated with the constructing the Kalman filter. To solve the second problem, the authors propose to apply the equations of parametric sensitivity. To localize the instants of the onset of such “discords”, the article proposes to apply the expansion of the parametric sensitivity functions in Fourier series with respect to the orthonormal wavelet basis.
The results of mathematical modeling of the solution of the problem of control and diagnostics of the simplest linear dynamical systems confirmed the operability of the proposed approach. Keywords: linear dynamical system, control points, parametric sensitivity equations, parametric sensitivity functions, wavelet analysis 

When laser ranging of a spacecraft the light impulse reflected from retroreflector , forms spot on the Earth surface, which center is usually located at a significant distance (from hundreds to thousands meters) from the station’s receiving telescope, due to the velocity aberration effect. Thus, the receiving telescope appears to be at periphery of the spot.
Due to the fact, that the electromagnetic radiation energy flow in the pulse decreases as distancing from the pulse axis to its periphery, only a small portion of the light energy hits the receiving telescope. Often, this portion is not enough to register the moment of the reflected impulse arrival at the laser station. To eliminate this shortcoming the Research and production Corporation “Systems of precision instrument making” suggested the retroreflector of a new type, in which maximum of intensity of the reflected impulse’ direction diagram was shifted from optical axis to periphery by coating the retroreflector edges with various coatings, so that the spot changed into a luminous ring. It allowed shifting the intensity maximum to about 1.2 arcseconds from the reflector optical axis with angular width at the level of halfpower of about one arcsecond.
Mathematical modeling and numerical analysis of a new type retroreflector implementation effectiveness for laser ranging of highorbit and loworbit spacecraft were performed in this work. The conducted study revealed that ensuring the most favorable conditions for loworbit spacecraft ranging (the orbit height of 300−550 km) in retroreflctor of a new type requires shifting of annular directional diagram maximum of the reflected impulse relative to the central beam not by 1.2 arcseconds, but several times more, i. e. approximately by 9.7 arcseconds. Highorbit spacecraft (orbit height of 6000−34000 km) for the same purpose must be equipped with retroreflectors of a new type, in which the maximum of the directional diagram of the reflected impulse is shifted relative to the Central beam by about five arcseconds.
This means that at the stage of designing of each spacecraft the unique retroreflector of a new type should be developed and manufactured maximally effective for operation at the projected orbit. Keywords: retroreflector, loworbit spacecraft, highorbit spacecraft, laser ranging, high intensity 