## Vol 15, No 1 (2016)

**Year:**2016**Articles:**24**URL:**https://journals.ssau.ru/vestnik/issue/view/144

### Full Issue

###### Abstract

The problem of selecting the parameters of nanosatellite separation from the launch vehicle orbital stage is formulated. The possibility of hazardous proximity of the nanosatellites to each other and to the orbiter of the “Soyuz” launch vehicle is analyzed. Expressions for determining the mathematical expectation and dispersion of the initial conditions of nanosatellites’ separation from the orbital stage are obtained as well as expressions for determining the mathematical expectation and dispersion of the nanosatellites’ position coordinates. The region of permissible parameters of nanosatellites’ separation that eliminate the risk of dangerous approaching of two nanosatellites both with the orbital stage and with each other is defined. The region of separation parameters eliminating the possibility of nanosatellites flying apart from each other to a distance of over 10 km in the course of two orbit flights is also determined. Recommendations on the choice of initial conditions of nanosatellite separation are given.

**VESTNIK of Samara University. Aerospace and Mechanical Engineering**. 2016;15(1):9-17

###### Abstract

Modal testing is an efficient tool for checking and updating of computational dynamic models of aircraft. Test objects are fixed by special elastic suspension systems during the modal testing time. Stiffness characteristics of such systems are determined on the assumption that the impact of the suspension on the eigentones of elastic vibrations of a freely flying aircraft should not exceed the pre-arranged level. It is therefore considered that the vibration frequency of the structure as a rigid body on the suspension should be several times lower than the natural frequency of the first flexible mode. Besides, different sources recommend various ratios between these frequencies. As to the modal testing of large flexible space structures, the task of creating such a suspension becomes many times more difficult because such structures can have very low natural frequencies of flexible modes. The influence of the suspension system on the accuracy of the aircraft modal testing results manifests itself in two ways. On the one hand, the use of the suspension leads to an increase of all natural frequencies of the test object. On the other hand, the occurrence of modes of the object as a rigid body with non-zero frequencies leads to the aircraft phase resonance frequency shifts which determine the natural frequencies of flexible mode tones. The paper presents a technique for correcting an aircraft computational dynamic model taking into account the suspension system. The correction is based on the fact that the errors in measurement of displacements in modal tests (i.e. eigenmodes as well) are greater than the errors in determining natural frequencies by more than an order of magnitude. The effect of modes of an object as a rigid body on an elastic suspension system on the accuracy of determination of its natural frequencies, generalized masses and generalized damping factors of flexible modes is analyzed.

**VESTNIK of Samara University. Aerospace and Mechanical Engineering**. 2016;15(1):18-27

###### Abstract

Тhis article describes the concept of designing a pneumatic-hydraulic system of feeding fuel components to a liquid-propellant rocket engine based on mathematical models and the system approach. There are three levels of designing: the first level is that of designing separate components of the fuel feed system- at this level physical processes in the system’s components are considered, their characteristics and external interactions are modeled; the second level is that of subsystems –at this level the process of interaction between the system’s elements is considered, internal connections between the elements and external interconnections of the system’s subsystems are modeled; the third level is that of the fuel feed system as a whole -at this level the process of interaction between the subsystems is considered, internal connections between the subsystems and external connections with the engine and other systems are modeled. A multilevel mathematical model of the fuel feed system was constructed. On the basis of the model an emergency situation (a faulty element) is modeled and the element is replaced, with its characteristics in the subsystem of feeding the oxidizer to the engine being changed; the dependence of the damper blow-down parameters on the rate of change in the input flow to the engine in the course of its starting is obtained. The mathematical model is associated with resultant documents, which makes it possible to get a modified set of documentation automatically when changes are introduced in the engine fuel feed system.

**VESTNIK of Samara University. Aerospace and Mechanical Engineering**. 2016;15(1):28-37

###### Abstract

Currently, creation of space -based P-band radar systems is a vital problem in the development of Earth remote sensing systems. These systems make it possible to solve the problem of monitoring vegetation on the Earth’s surface, to carry out soil analysis and detect objects detecting hidden in foliage. Such systems are, however, difficult to produce due to the necessity of using large- aperture antenna systems. Expanding active phased arrays and reflector antennas are most common for the task. Structures of this kind are characterized by considerable mass and dimensions, which does not make it possible to regard small satellites as their carriers. A system with an array of four transceiving Yagis is proposed. The systems are shown to possess sufficient characteristics to solve the target tasks. The structure’s simplicity makes it possible to install the systems on small satellites, which drastically reduces the cost and time of production.

**VESTNIK of Samara University. Aerospace and Mechanical Engineering**. 2016;15(1):38-45

###### Abstract

The problem of stabilizing the motion of small spacecraft relative to the center of mass in the process of deploying an orbital tether system is presented in the paper. Stabilization is carried out with respect to the direction of the tether and is characterized by the classical Euler angles (precession, nutation and proper rotation). The proposed method of suboptimal control is based on the joint application of the principle of Bellman's dynamic programming and the averaging method. The integral quadratic optimality criterion that depends on operating deviations and low control inputs is used. Control synthesis is accomplished using the model of angular motion recorded for small angles of nutation. An example of calculating optimal control of an orbital tether system deployed for the purpose of de-orbiting small satellites to the Earth is given. The efficiency of the optimal control arrived at is confirmed by numerical calculations for the basic nonlinear model of motion of an orbital tether system.

**VESTNIK of Samara University. Aerospace and Mechanical Engineering**. 2016;15(1):46-54

###### Abstract

The paper deals with the problem of choosing the type and the main design parameters of the correcting propulsion system of spacecraft functioning in low near-circular Earth orbits. The efficiency of using chemical (impulse) and low-thrust electric propulsion engines is analyzed. Analytical relations for calculating spacecraft design parameters and specifying the areas of efficient use of electric propulsion engines are obtained for the criterion of useful load fraction and the assumption of constant power dependent acceleration. The results of calculating the areas of efficient use and design parameters of spacecraft for various operational altitudes are shown.

**VESTNIK of Samara University. Aerospace and Mechanical Engineering**. 2016;15(1):55-63

###### Abstract

The problem of modeling the operation of special equipment intended for modeling orbital tether system deployment is studied. During the deployment of an orbital tether system the tether tension force control program is used that takes into account limitations on the deployment velocity. A parametric boundary problem is solved for the program of controlling the deployment of an orbital tether system. A kinematic scheme of the equipment, consisting of an engine that simulates the Earth’s gravitation and a tether deployment mechanism, is created. Based on the kinematic scheme, a dynamic scheme with control path feedback on tether deployment velocity and tether tension is created. The deviation control principle is implemented: control is realized on the deviation of the real value of the parameter under consideration from its program value. The magnification ratio of the controlled value deviation from the program values is used as the controlled value in transient optimization. The numerical simulation of the test bench operation performed in the MapleSim 7 environment shows acceptable quality of transient tether deployment velocity and tether tension.

**VESTNIK of Samara University. Aerospace and Mechanical Engineering**. 2016;15(1):64-72

###### Abstract

The paper presents various schemes of flight of a separated part of the first stage, equipped with the reactive recovery system taking a two-stage oxygen-kerosene medium class launch vehicle assembled on the basis of the results of ballistic design and similar to the“Falcon-9” launcher in its power mass characteristics. The results of assessing the change in the payload mass placed into the low-earth orbit by the launcher, estimating the change in the value of the mass ratio of the first-stage recovery system and limit values of aerodynamic and heat loads of the first stage in the phase of recovery depending on the flight scheme are presented. The values of the mass ratio of the recovery system depending on the flight scheme are compared with that of the mass ratio of an aircraft-type recovery system. The advantages of the reactive recovery system in comparison with the aircraft-type recovery system are pointed out. The necessity of using an additional retroburn by restarting the service propulsion system of the stage prior to the re-entry with the aim of reducing aerodynamic and heat loads. It is shown that the reactive way of recovery can be implemented with acceptable energy losses only by making an intermediate landing on the complex located along the flight course.

**VESTNIK of Samara University. Aerospace and Mechanical Engineering**. 2016;15(1):73-80

###### Abstract

Thermal design is a prerequisite essential to design a satellite. In space environment, it makes it possible for the satellite to survive in extreme hot and cold conditions. In recent years small satellite missions have been developed for many kinds of purposes. The paper describes thermal design for the “AIST” small spacecraft mission. To calculate thermal environment a detailed thermal mathematical model has been developed using the finite element method and Siemens NX 10.0 software with the integrated module NX Space Systems Thermal Simulation. The analysis carried out with the help of mathematical simulation showed the sufficiency of the passive thermal control system of the “AIST” small spacecraft. In order to improve thermal radiation couplings between panels a coating with a high emissivity factor was applied on all the inner surfaces. The outer surfaces (except the areas occupied with photovoltaic converters) were coated with aluminum foil. The graphs of changes in temperatures of onboard equipment in the orbital flight phase show that all the parameters meet the requirements of the thermal control system specifications.

**VESTNIK of Samara University. Aerospace and Mechanical Engineering**. 2016;15(1):81-88

###### Abstract

The paper presents an algorithm of damping the initial angular rate of the SamSat-218D nanosatellite after its separation from the transporting-launching container. Three mutually orthogonal magnetic coils are used as actuators that provide damping of the initial angular rate on board the nanosatellite. The traditional B-dot algorithm is used as the damping algorithm. Two operating modes are possible for the B-dot algorithm: a continuous mode and a discrete one. As the continuous operating mode of the magnetic coils onboard the nanosatellite in orbital flight is inexpedient because of the necessity of measuring the Earth magnetic field intensity vector the discrete mode of operating of the algorithm of damping the initial angular velocities acquired by the nanosatellite after its separation from the transporting-launching container is analyzed. The results of the mathematical simulation during the analysis of choosing discretization intervals in the algorithm of damping the initial angular rate of the SamSat-218D nanosatellite are presented.

**VESTNIK of Samara University. Aerospace and Mechanical Engineering**. 2016;15(1):89-96

###### Abstract

The problem of developing a nanosatellite attitude control system using three reaction wheels mounted along the main central axes of inertia is discussed in the paper. The law of controlling a nanosatellite’s attitude is based on a PD - controller. The stability of the process of controlling the nanosatellite attitude using the Lyapunov function method has been analyzed. It allows us to prove that the obtained control law provides the asymptotic stability of nanosatellite angular motion. Hereafter, the function of control voltage for electric motors of reaction wheels taking into account their specifications is obtained based on the developed mathematical model of reaction wheel dynamics. Numerical calculations of controlled angular motion have been carried out for the nanosatellite CubeSat3U with actuators on the basis of a commercial DC motor. Several cases of controlling the satellite’s rotation by different angles are considered in the course of the numerical experiments. The results of numerical experiments showed the adequacy of the developed mathematical model.

**VESTNIK of Samara University. Aerospace and Mechanical Engineering**. 2016;15(1):97-106

###### Abstract

The paper presents the results of an experiment using the «Space system of microacceleration compensation» (SSMC) scientific hardware. The SSMC hardware has been developed and manufactured at the Institute of Space Device Engineering of Samara State Aerospace University with the participation of the Joint Stock Company «Space Rocket Center «PROGRESS» and operated on the Photon-M №4 spacecraft in the period from July 18 to September 1, 2014. The experiment is dedicated to collecting information about the values of the magnetic field of the Earth and compensating accelerations by comparing the measured values with the calculated values for IRGF model. Characteristics of the SSMC scientific hardware and the basic data obtained in the analysis of telemetry data are presented. An averaged picture of distribution of the magnetic field of the Earth during the experiment is obtained.

**VESTNIK of Samara University. Aerospace and Mechanical Engineering**. 2016;15(1):107-114

###### Abstract

Small spacecraft (SSC) is exposed to fluxes of micrometeoroids and space debris during its flight in space environment. These effects may result in the destruction of the SSC. The article describes the design of the SSC for the registration of micrometeoroids and space debris. The SSC is made up of the orientation system, detectors of micrometeoroids and space debris particles based on microchannel plates. A 3D-model of SSC has been developed and its full-scale mockup has been made. The method of measuring registration of micrometeoroids and space debris particles is based on the measurement of the ion current of shock plasma that is formed in the particle’s hypervelocity impact with the detector target (solar batteries and the film stretched between them). The great area of the detector target increases the probability of its interaction with high-velocity micro-particles and increases the efficiency of the detector.

**VESTNIK of Samara University. Aerospace and Mechanical Engineering**. 2016;15(1):115-121

###### Abstract

The article discusses the option of using video images to determine the orientation and the position of the second nanosatellite relative to the first one by a series of snapshots made by the first nanosatellite. Optical cameras installed on the first nanosatellite are used as measuring devices. A new approach has been developed to solve the task set. The approach includes an image processing algorithm, a genetic algorithm of differential evolution and a model of motion relative to the center of mass. The approach takes into account the requirements imposed on the nanosatellite hardware that sets limitations on the computational resource of the airborne digital computer and on the quality of images obtained from the optical camera. The developed approach is more economic than similar algorithms. The approach was verified by the benchmark problem of separating two nanosatellites in a short time interval. The dependence of the coordinates of the center of mass of the second satellite on the current orientation and pixel orientation target coordinates in the shot is revealed. The paper includes graphs of the error of determining orientation and position of the center of mass of the second satellite relative to the first one. The approach demonstrates acceptable accuracy in the range of up to 10 seconds for the problem under consideration. The accuracy decreases dramatically as the distance between the two nanosatellites increases.

**VESTNIK of Samara University. Aerospace and Mechanical Engineering**. 2016;15(1):122-131

###### Abstract

Existing radar aids for the research of the ionosphere and ionosondes allow only local diagnostics of the ionosphere. Creating a network of traditional tools of radio sounding of ionosphere is quite difficult and expensive. Using constellations of LEO satellites in ionospheric radio-tomography problems is today a promising direction of ionospheric research that allows getting the latest update about its condition. It is necessary to develop new, highly efficient methods and tools for solving problems of this class. An approach for the reconstruction of vertical distribution of ionospheric electron density by processing satellite-to-satellite signals is discussed in the article. The form of a promising orbital constellation of small satellites that makes it possible to obtain the cross section of the ionospheric electron density in the plane of the orbit is determined. It was found that the problem of 2D reconstruction of electron density vertical distribution in the ring layer of the ionosphere can be solved during the orbital period of the satellite in the constellation, the number of satellites in which is 5 to 7, depending on the height of the orbit. It is shown that as the number of vehicles in the constellation increases up to the amount that fills the orbit, the reconstruction time could be reduced to 10 minutes. It is shown that the problem is reduced to a few-view tomography problem using the method of convolutional filtering.

**VESTNIK of Samara University. Aerospace and Mechanical Engineering**. 2016;15(1):132-138

###### Abstract

The paper presents technologies of reducing the technological environmental impact of man-made space launch vehicles (SLV) based on controlled descent and trajectories of deorbiting the spent stages, burning of the separated nose fairing halves and tail section in the atmosphere. Controlled descent of a spent stage is accomplished due to the installation of an active on-board recovery system that uses unexpended remnants of the liquid components of propellant in the tanks. The burning of the fairing and tail section is based on the introduction of pyrotechnic compositions in their designs. Practical possibility of implementing this technology is shown taking the SLV «Soyz-2.1.b» space rocket as an example. It makes it possible not only to provide a solution to the basic environmental requirements, but also to improve the performance characteristics of the SLVs, move to a new technical level of their designing and operation. Using the technology of gasification of liquid residual propellants allows controlled descent of separating SLV stages with the scatter of impact points less than1 km, displacement of the impact range to 15% and increasing the mass of the payload due to the maneuver of the SLV lower stage to the intended impact area to 5% of the initial payload mass. The mass of additional equipment required for the implementation of this technology can be up to 3-5% of the «dry» structure of the SLV separating part.

**VESTNIK of Samara University. Aerospace and Mechanical Engineering**. 2016;15(1):139-150

###### Abstract

The paper presents the results of improving the Stewart platform control system by applying the second-order regulation law to pneumatic drive controllers and transformation of the actuating signal for the functioning of valves in the linear region of the flow characteristic. Methods of mathematical and numerical simulation using the software package MatLab/Simulink and AMESim are used to analyze the sufficiency of the measures proposed. Special attention is given to the analysis of the pneumatic drive dynamic characteristics. Dynamic characteristics of the pneumatic drive control system incorporated in the Stewart platform are calculated, which show the efficiency of the proposed methods of improvement. If the pneumatic drive is used as part of the Stewart platform the load in the output component can reach hundreds of kilograms, which makes it possible to use it both for dynamic tests of the systems and for positioning objects, for instance, mobile simulators.

**VESTNIK of Samara University. Aerospace and Mechanical Engineering**. 2016;15(1):151-162

###### Abstract

Elastic-damping supports are widely spread in the design of aviation gas-turbine engines. These supports include elastic elements of the «squirrel cage» type. A methodology of calculating the flexibility matrix for the «squirrel cage» with straight rod elements of rectangular cross-section with account for groove rounding is presented in the paper. Determining the flexibility matrix is essential for constructing mathematical models of aviation gas turbine engines when solving problems of rotor dynamics. The methodology is based on the application of Mohr integral for beam constructions. The results obtained with the help of the methodology are compared with the results of calculations in the finite-element complex and with the results of calculation without regard for the rounding, as well as with results obtained by other authors.

**VESTNIK of Samara University. Aerospace and Mechanical Engineering**. 2016;15(1):163-170

###### Abstract

The paper presents the analysis of the possibility of using the information resource of the Globalstar LEO satellite communication system (LSCS) for rapid data exchange via the following channels: MCC – Globalstar – nanosatellite, nanosatellite – Globalstar – nanosatellite in order to receive telemetric information from a nanosatellite, to transmit necessary commands and information from MMC to a nanosatellite as well as to exchange data between two nanosatellites. The possibility of data transmission via the channels: MCC – Globalstar – nanosatellite, nanosatellite – Globalstar – nanosatellite is shown. The duration of communication sessions via the channel MCC – Globalstar – nanosatellite and the channel nanosatellite – Globalstar – nanosatellite is analyzed Potential volumes of data transmitted between two nanosatellites are determined. Stochastic analysis of the possibility of data transmission between two spacecraft is performed and the possibility of data transmission between two spacecraft, depending on the data volume and load level of the Globalstar system is assessed.

**VESTNIK of Samara University. Aerospace and Mechanical Engineering**. 2016;15(1):171-179

###### Abstract

The main principles of choosing the capacity of a high-speed radio data link for modern Earth remote sensing spacecraft are discussed in the paper. The following points are taken into account: overfilling of the onboard memory storage device; duration of communication sessions between the spacecraft and the downlink point; the required bandwidth and the reliability of the radio data link. Mathematical restrictions for the conditions of the overflow of the on-board memory storage of target information and the amount of information transmitted to the downlink points during a communication session between the spacecraft and the downlink point are specified. An expression is proposed for the estimation of radio data link capacity on the basis of the Shannon formula with account for the energy relations for satellite communication links, the required width of the passband and the probability of data transmission error. The influence of the probability of the information transmission error and the main parameters of the radio signal (the speed of protective coding and the phase deviation) on the value of high-speed radio data link capacity is analyzed. Changes in radio data link capacity in retrospect for the years immediately ahead are analyzed in accordance with the predicted value of the required volume of space information of Earth remote sensing for radio data links of different reliability.

**VESTNIK of Samara University. Aerospace and Mechanical Engineering**. 2016;15(1):180-186

###### Abstract

Using a combination of the method of invariance of pulse characteristics of dynamic systems and the method of parametric synthesis is proposed for time sampling in nonlinear models of oscillatory systems. The difference equation of motion and the block diagram of a linear dissipative oscillator form the basis for the solution of the problem of designing a nonlinear discrete system (discrete mapping). Thus, Van der Pol, Rayleigh, Duffing oscillators are introduced as objects of nonlinear dynamics with discrete time mappings. Characteristics of self-oscillations of discrete and analog Van der Pol oscillators are compared, their similarity and difference at high levels of excitation is established. The results of a numerical experiment with a discrete Van der Pol – Duffing oscillator made it possible to establish that it can operate in two modes of self-oscillations differing in amplitudes and frequencies. It is shown that the transition between the modes can be followed by the generation of chaotic self-oscillations as the system parameters vary. Possible areas of application of the discrete dynamic systems described in the article are identified.

**VESTNIK of Samara University. Aerospace and Mechanical Engineering**. 2016;15(1):187-196

###### Abstract

A prototype of the hyperspectrometer based on the Offner scheme has been tested. Drawings have been produced and the main mirror elements of the hyperspectrometer including diffraction grating on a convex spherical surface have been fabricated. The profile of the grating groove has been measured and light energy distribution in diffraction orders has been modeled as a function of wavelength. Optomechanical elements for the necessary alignments of the hyperspectrometer elements have been designed and manufactured. Adjustment of the optical prototyping scheme has been implemented and point images for three wavelengths of monochromatic radiation have been obtained. Distribution of light energy in diffraction orders and maxima positions are in an agreement with the simulation results. The spectrometer has also been tested on test images in polychromatic radiation under the control of the developed software.

**VESTNIK of Samara University. Aerospace and Mechanical Engineering**. 2016;15(1):197-206

###### Abstract

The problem of fuel sloshing in the measuring cylindrical channel of the system controlling fuel expenditure in the tank is considered in the paper. The system under consideration is a tank inside which there is a measuring channel in the form of a vertical cylindrical tube. The fuel level in the tank is recorded by the level sensors disposed within the measurement channel. It is known that the level of fuel in the tank does not match that in the channel. A mathematical model of fuel flow in the channel is constructed on the basis of parabolic equations of the heat-conduction type. The numerical solution of the model for the Crank-Nicolson scheme is presented. To confirm the results obtained by the model, the problem is solved with the help of full Navier-Stokes equations and the VOF model in the Ansys Fluid package. Construction of geometrical patterns and block grids in the ICEM CFD package is described. The problem is solved on grids differing in volume. The comparison of the results shows good agreement between them and indicates the presence of quasi-periodic oscillations of fuel in the channel. The inertia of the liquid column is the cause of the mismatch between the free surface level in the tank and that in the channel. When conditions change on the boundary, the response is late in the channel, causing vibrations. The results obtained suggest that the level sensors evenly spaced along the length of the channel will provide distorted information. The error is not systematic. The proposed model can be used to estimate the sloshing of liquid fuel in the measuring channels of fuel expenditure control system and for the development of more complex models.

**VESTNIK of Samara University. Aerospace and Mechanical Engineering**. 2016;15(1):207-217

###### Abstract

The paper deals with the possibility of application of generic concepts based on the use of multiple programming paradigms with the aim of providing uniform access to universal data storage. The investigation is conducted using the example of developing a library of software components within the framework of the project of creating an expert system using the information base of the Topos Pro software package. The aim of the paper is to check the possibility of forming mechanisms for construction of independent components for access and data processing that would make it possible to produce software products with a low level of coupling and high cohesion. In this case, the concrete implementation would be characterized by conceptual integrity and would provide better understanding of the design process. Storage structures and data access facilities should be associated with what is considered in the article as generic concepts of container class adapters and iterators. This makes it possible to present the program code as a set of elementary independent primitives forming the basis for application logic design in terms of generic abstractions implying the process of extending library components and their adaptation to the domain area. The approach of using multiple programming paradigms coupled with the possibility of extension and setting of newly-created components based on library abstractions provides a new level of understanding programming. The generic concepts in this case become the main tools, while implementations of specific classes on their basis can be set through the use of overloading, aggregation, inheritance and specification of requirements for an abstract data type. After the pre-implementation of some library components and specific classes of access to a universal data model a conclusion can be made that the chosen strategy of interaction with the universal storage based on generic concepts is the best. It makes possible to reduce the complexity level as well as the LOC and allows the developer to concentrate only on the domain logic of applications providing access to the databases supporting the universal data model.

**VESTNIK of Samara University. Aerospace and Mechanical Engineering**. 2016;15(1):218-227