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Abstract The results of repeated processing of magnetic measurements carried out on the Photon-12 satellite (which was in orbit from September 9 to 24, 1999) are described. The processing was performed in order to reconstruct the uncontrolled rotational motion of this satellite. In re-processing, the simplified mathematical model of rotational motion was used. The actual orbit of a satellite (the apogee height is 380 km, the perigee height is 220 km) is replaced by a circular orbit; the expression for the aerodynamic moment acting on a satellite is simplified. The system of differential equations underlying the new model is autonomous and proved to be sufficiently accurate to reconstruct the satellite motion based on magnetic measurements in the case in which the satellite angular velocity was not very low and grew gradually. In the last third of the flight, when the satellite motion became virtually stable and had a sufficiently high angular velocity, this system could be reduced to a generalized-conservative system. Such a reduction makes more definite the set of its solutions suitable for approximate description of the actual motion of a satellite. In some segments of motion, the combining of which covers about 3 days, it was possible to use, for this purpose, the periodic solutions continued from the Lyapunov periodic solutions.

The results of reprocessing of magnetic measurements performed on the Foton-12 satellite (in orbit on September 9–24, 1999) are described. The processing was carried out in order to reconstruct the uncontrolled rotational motion of this satellite. The reprocessing used a simpler mathematical model of the rotational motion than the processing performed shortly after the flight. The simplifications were made in such a way that the new model was accurate enough to match the models used by V.V. Beletskiy when studying the evolution of the uncontrolled rotational motion of a satellite in the case in which this motion is close to the regular Euler precession of an axisymmetric rigid body. The results of processing measurements in 25 short (3.5 h) time intervals were directly compared with the averaged equations arising in Beletskiy’s theory. The evolution of the Foton-12 motion is well described by these equations in the second half of the flight, when the angular velocity of the satellite was within 0.8°–1.0°/s.

The possibility of stabilizing the gravitational orientation mode of a massive artificial Earth satellite (AES) by the torque produced by electromagnets interacting with Earth’s magnetic field is shown. As an example, the control of rotational motion of the satellite like Bion M-1 and Foton M-4 is considered. Control is accomplished by changing the currents in the electromagnets. The control law is considered, which provides damping of the disturbed motion of a satellite and its stabilization in the gravitational orientation mode. To form this law, it is sufficient to have the readings of a triaxial magnetometer and of an angular velocity sensor. The control law efficiency is verified by mathematically modeling satellite motion relative to the center of masses, under an effect of gravitational and aerodynamic torques, as well as the torque produced by electromagnets.

The uncontrolled rotational motion of Progress MS-07 and Progress MS-08 transport cargo spacecraft in the mode of gravitational orientation of a rotating satellite was reconstructed. Modes were implemented in April and August 2018. The reconstruction was conducted using an integral statistical method according to measurements of spacecraft angular velocity. Measurement data obtained at a certain time interval were processed together with the least squares method by integrating the equations of spacecraft motion relative to the center of mass. As a result of processing, the initial conditions of motion and parameters of the used mathematical model were estimated. The correctness of the reconstruction was checked by measuring the current taken from the solar panels. In the mode of gravitational orientation, the spacecraft rotated around its longitudinal axis with an angular velocity of 0.1–0.2 deg/s oscillating relative to the local vertical.

The results of the reprocessing of magnetic measurements described below were performed with onboard sensors on the Foton M-2 satellite (orbiting May 31 - June 16, 2005). Processing was carried out in order to reconstruct the uncontrolled rotation. The reprocessing used a simpler mathematical model of rotational motion in comparison with the processing carried out immediately after the flight. Simplifications were made so that the new model matched the models used by V.V. Beletsky in his theoretical analysis of the evolution of the uncontrolled rotational motion of a satellite in the case when this motion was close to the regular Euler precession of an axisymmetric rigid body. As a result, due to some coarsening of the reconstruction, it was possible to directly compare the obtained experimental results with the theory and analyze them.

Построена математическая модель стенда натурных динамических испытаний акселерометров, созданного в ИПМ им. М.В. Келдыша РАН. Стенд имеет подвижную платформу с одной степенью свободы. Платформа может вращаться вокруг неподвижной вертикальной оси. К платформе жестко крепятся тестируемые блоки акселерометров, и ей придается варьируемое в широких пределах вращение. Фактическое изменение угла поворота платформы реконструируется апостериори по видеоизображению, получаемому с помощью системы технического зрения. Реконструкция выполняется численно, что позволяет рассчитать реальные ускорения, испытываемые акселерометрами. Рассчитанные ускорения сравниваются с цифровыми данными измерений. По результатам сравнения выполняются тестирование и калибровка чувствительных элементов акселерометров, электронных блоков и т.п.

The paper presents the reconstruction results of rotational motion of the AIST-2D small spacecraft by onboard measurements of vectors of angular velocity and the strength of Earth’s magnetic field obtained in summer 2016. The reconstruction method is based on the reconstruction of kinematic equations of the rotational motion of a solid body. According to the method, measurement data of both types collected on a certain time interval are processed together. Measurements of the angular velocity are interpolated by piecewise-linear functions, which are replaced in kinematic differential equations for a quaternion that defines the transformation from the satellite instrument coordinate system to the inertial coordinate system. The obtained equations represent the kinematic model of the rotational motion of a satellite. A solution to these equations that approximates the actual motion is derived from the condition of the best (in the sense of the least squares method) match between the measurement data of the strength vector of Earth’s magnetic field and its calculated values. The initial conditions of the approximating solution, constant bias in angular velocity measurements, and angles specifying the matrices of transformation from magnetometer intrinsic coordinate systems to the instrument coordinate system of the satellite (measurements of the angular velocity are specified in it) are refined. The described method makes it possible to reconstruct the actual rotational motion of a satellite using one solution of kinematic equations over time intervals longer than 10 h.

A second-order differential equation containing a large parameter is considered. Such an equation can be interpreted as an equation of constrained oscillations of a mechanical system with one degree of freedom, provided that the fundamental frequency of the system substantially exceeds the external frequency. We provide a new proof of the existence of a periodic solution of that equation such that it is close to the periodic solution of the corresponding degenerate equation. That proof is obtained by means of the Poincare method.

The solar orientation mode of an artificial Earth satellite is investigated. Satellite parameters correspond to the parameters of the Bion M and Foton M-4 satellites. In this mode, the normal to the satellite solar cell plane is always directed to the Sun, the longitudinal axis lies in the plane of the orbit, and the satellite absolute angular velocity is very small. The mode is stabilized by electromagnets that interact with the Earth magnetic field and a rotating flywheel that generates a constant gyrostatic moment along the satellite longitudinal axis. Such a moment can be generated using a reaction wheel system. The constancy of the gyrostatic moment means that this system will operate without saturation. The satellite attitude control is implemented by changing the currents in the electromagnets. Two control laws that reduce the satellite angular velocity and stabilize the solar orientation are investigated. Their implementation does not require complex measurements. It is sufficient to have the readings of a solar sensor and a triaxial magnetometer and equipment for their processing. The effectiveness of control laws is confirmed by the mathematical modeling of the satellite motion with respect to the center of mass under the influence of gravitational and aerodynamic moments, as well as the moment generated by electromagnets.

We investigate the periodic systematic error found in ground-based measurements of the BOKZ-M60 star sensor. This error can be explained by the periodic pixel structure of the sensor CCD matrix. Our conclusion is based on processing a sufficiently long series of measurement data. The measurements are processed in a few stages. First, we approximate the stellar sky motion on the matrix plane using an appropriate mathematical model. Then, we trace the motion of some particular stars relative to the model sky motion. Using spectral analysis, we then find the periodic components of their motion. The period of those components allow us to make the conclusion given above.

We investigate the precision in the readings of the star tracker BOKZ-M60 obtained in the dynamic field testbed of the Space Research Institute of the Russian Academy of Sciences (SRI RAS). The testbed features a mobile platform, on which a star tracker is mounted, which scans the starry sky. The platform movement is controlled by a PC, however, the values of the rotation angles in the platform hinges are not known with the desired degree of accuracy. In testing star trackers, the error in the known platform orientation must be around 1″, which corresponds to an error in determining the linear coordinates of the platform reference points of less than 3 μm. It is difficult and expensive to organize outside measurements of the movement of a mobile object with such accuracy. For this reason, the following accuracy estimation scheme is used. We consider comparatively long series of the determined orientation parameters obtained by the tracker in the testbed. With the help of a suitable mathematical model, a detailed reconstruction of the actual rotational motion of the tracker is performed based on these measurements. In this reconstruction, the residuals in the tracker readings are calculated. Based on the analysis of the residuals, conclusions are drawn about the accuracy of the tracker. As it turns out, the accuracy of determining the optical axis of the tracker lens depends on the angular velocity of the platform and lies in the range from 2″ to 25″

The BOKZ-M60 star sensor (Unit for Measuring Star Coordinates) is intended for determining the parameters of the orientation of the axes of the intrinsic coordinate system relative to the axes of the inertial system by observations of the regions of the stellar sky. It is convenient to characterize an error of the single determination of the orientation of the intrinsic coordinate system of the sensor by the vector of an infinitesimal turn of this system relative to its found position. Full-scale ground-based tests have shown that, for a resting sensor the root-mean-square values of the components of this vector along the axes of the intrinsic coordinate system lying in the plane of the sensor CCD matrix are less than 2″ and the component along the axis perpendicular to the matrix plane is characterized by the root-mean-square value of 15″. The joint processing of one-stage readings of several sensors installed on the same platform allows us to improve the indicated accuracy characteristics. In this paper, estimates of the accuracy of systems from BOKZ-M60 with two and four sensors performed from measurements carried out during the normal operation of these sensors on the Resurs-P satellite are given. Processing the measurements of the sensor system allowed us to increase the accuracy of determining the each of their orientations and to study random and systematic errors in these measurements.

We have reconstructed the uncontrolled rotational motion of the Progress M-29M transport cargo spacecraft in the single-axis solar orientation mode (the so-called sunward spin) and in the mode of the gravitational orientation of a rotating satellite. The modes were implemented on April 3–7, 2016 as a part of preparation for experiments with the DAKON convection sensor onboard the Progress spacecraft. The reconstruction was performed by integral statistical techniques using the measurements of the spacecraft’s angular velocity and electric current from its solar arrays. The measurement data obtained in a certain time interval have been jointly processed using the least-squares method by integrating the equations of the spacecraft’s motion relative to the center of mass. As a result of processing, the initial conditions of motion and parameters of the mathematical model have been estimated. The motion in the sunward spin mode is the rotation of the spacecraft with an angular velocity of 2.2 deg/s about the normal to the plane of solar arrays; the normal is oriented toward the Sun or forms a small angle with this direction. The duration of the mode is several orbit passes. The reconstruction has been performed over time intervals of up to 1 h. As a result, the actual rotational motion of the spacecraft relative to the Earth–Sun direction was obtained. In the gravitational orientation mode, the spacecraft was rotated about its longitudinal axis with an angular velocity of 0.1–0.2 deg/s; the longitudinal axis executed small oscillated relative to the local vertical. The reconstruction of motion relative to the orbital coordinate system was performed in time intervals of up to 7 h using only the angularvelocity measurements. The measurements of the electric current from solar arrays were used for verification.

The paper has studied the accuracy of the technique that allows the rotational motion of the Earth artificial satellites (AES) to be reconstructed based on the data of onboard measurements of angular velocity vectors and the strength of the Earth magnetic field (EMF). The technique is based on kinematic equations of the rotational motion of a rigid body. Both types of measurement data collected over some time interval have been processed jointly. The angular velocity measurements have been approximated using convenient formulas, which are substituted into the kinematic differential equations for the quaternion that specifies the transition from the body-fixed coordinate system of a satellite to the inertial coordinate system. Thus obtained equations represent a kinematic model of the rotational motion of a satellite. The solution of these equations, which approximate real motion, has been found by the least-square method from the condition of best fitting between the data of measurements of the EMF strength vector and its calculated values. The accuracy of the technique has been estimated by processing the data obtained from the board of the service module of the International Space Station (ISS). The reconstruction of station motion using the aforementioned technique has been compared with the telemetry data on the actual motion of the station. The technique has allowed us to reconstruct the station motion in the orbital orientation mode with a maximum error less than 0.6° and the turns with a maximal error of less than 1.2°.

We have described an express technique for processing the results of experiments with a DAKON-M convection sensor on board the Service Module of the International Space Station (ISS) in 2011. The technique uses a certain rule to compare the sensor measurements with the calculated data on the quasistatic component of microacceleration at the point of installation. The sensor experiments have been conducted during shuttle docking and undocking, when low-frequency microaccelerations on the ISS were significant. The microaccelerations have been calculated using measurement data of the MAMS low-frequency accelerometer installed in the Lab module and the telemetry data on the ISS rotational motion. This has made it possible to convert the MAMS measurement data to the DAKON-M convection sensor installation point. A comparison of sensor readings with calculated microaccelerations has revealed fairly good agreement between them.

The results of reconstructing the uncontrolled rotational motion of the Aist small spacecraft prototype during its flight in early 2014 have been presented. The reconstruction was carried out by processing data from onboard measurements of the Earth’s magnetic field. The processing procedure used portions of data covering intervals of time with durations ranging from a few dozen minutes to three hours. Data obtained in each such interval were processed jointly by the least-squares method by integrating the equations of the satellite motion relative to the center of mass. The initial conditions of the motion and the parameters of the used mathematical model during processing have been estimated. The results of processing for several data intervals have provided a fairly complete picture of the satellite motion. This was the weakly disturbed Euler–Poinsot motion.

The mathematical model, which allowed us to reconstruct the rotational motion of the Bion M-1 and Foton M-4 satellites by processing the measurements of onboard magnetometers and the angular velocity sensor, is sufficiently detailed and accurate. If we slightly lower the requirements for accuracy and transfer to a rougher model, i.e., we will not update the biases in measurements of the angular velocity component, then the measurement processing technique can be significantly simplified. The volume of calculations in minimizing the functional of the least-square technique is reduced; the most complicated part of calculations is performed using the standard procedure of computational linear algebra. This simplified technique is described below, and the examples of its application for reconstructing the rotational motion of the Foton M-4 satellite are presented. A noticeable distinction in the reconstructions of motion, constructed by simplified and more exact techniques, is revealed in processing the measurements over time intervals longer than 4 hours.

The actual controlled rotational motion of the Foton M-4 satellite is reconstructed for the mode of single-axis solar orientation. The reconstruction was carried out using data of onboard measurements of vectors of angular velocity and the strength of the Earth’s magnetic field. The reconstruction method is based on the reconstruction of the kinematic equations of the rotational motion of a solid body. According to the method, measurement data of both types collected at a certain time interval are processed together. Measurements of the angular velocity are interpolated by piecewise-linear functions, which are substituted in kinematic differential equations for a quaternion that defines the transition from the satellite instrument coordinate system to the inertial coordinate system. The obtained equations represent the kinematic model of the satellite rotational motion. A solution of these equations that approximates the actual motion is derived from the condition of the best (in the sense of the least squares method) match between the measurement data of the strength vector of the Earth’s magnetic field and its calculated values. The described method makes it possible to reconstruct the actual rotational satellite motion using one solution of kinematic equations over time intervals longer than 10 h. The found reconstructions have been used to calculate the residual microaccelerations.

Quasi-static microaccelerations of four satellites of the Foton series (nos. 11, 12, M-2, M-3) were monitored as follows. First, according to measurements of onboard sensors obtained in a certain time interval, spacecraft rotational motion was reconstructed in this interval. Then, along the found motion, microacceleration at a given onboard point was calculated according to the known formula as a function of time. The motion was reconstructed by the least squares method using the solutions to the equations of satellite rotational motion. The time intervals in which these equations make reconstruction possible were from one to five orbital revolutions. This length is increased with the modulus of the satellite angular velocity. To get an idea on microaccelerations and satellite motion during an entire flight, the motion was reconstructed in several tens of such intervals. This paper proposes a method for motion reconstruction suitable for an interval of arbitrary length. The method is based on the Kalman filter. We preliminary describe a new version of the method for reconstructing uncontrolled satellite rotational motion from magnetic measurements using the least squares method, which is essentially used to construct the Kalman filter. The results of comparison of both methods are presented using the data obtained on a flight of the Foton M-3.

Angular motion of an axisymmetrical artificial satellite with a permanent magnet in the real magnetic field of the Earth was investigated. The satellite orbit was calculated taking into account the major perturbing factors, and the satellite dipole moment was parallel to the axis of symmetry. Satellite stationary motions were constructed, where this axis constituted a narrow angle with the Earth’s magnetic field vector. Possibility was demonstrated of approximating such motions by a sequence of periodic solutions of modified motion equations. Sequence composed of such solutions also approximated the spectrum of stationary motion.

The results of the reconstruction of uncontrolled attitude motion of the satellite Aist during its flight in May 2013 are presented. The reconstruction was performed by the processing of data from onboard measurements of the Earth’s magnetic field. The processing technique was applied to data segments covering time intervals of about 100 min. The data obtained at each such interval were processed jointly using the least squares method by integrating the equations of the satellite motion relative to its center of mass. When processing, the initial conditions of motion and parameters of the used mathematical model were estimated. The results of processing several data intervals made it possible to obtain sufficiently complete information about the motion of the satellite.

The BOKZ-M star sensor (a unit for measuring star coordinates) is intended to determine the parameters of the orientation of the axes of its own coordinate system relative to the axes of the inertial system using the observations of the areas of the stellar sky. A large number of factors influence the accuracy of this determination, and the estimation of the contribution of every factor to the total error is not always possible. In general, it must be limited by an estimation of the total error according to the results of studying a longterm series of determinations of the orientation parameters obtained in the ground tests and in space flight. This paper presents accuracy estimations for the BOKZ-M device obtained during its flight operation on the Meteor-M satellite.

Actual controlled rotational motion of the Bion M-1 satellite is reconstructed for the modes of the orbital and single-axis solar orientation. The reconstruction was performed using data of onboard measurements of the vectors of angular velocity and the Earth’s magnetic field (EMF) strength. The reconstruction procedure is based on the kinematic equations of the rotational motion of a solid body. In the framework of this procedure, measurement data for two types collected at a certain time interval are processed jointly. Measurements of angular velocity are interpolated by piecewise–linear functions, which are substituted in the kinematic differential equations for quaternion giving the transition from the satellite instrument coordinate system to the inertial (the second geoequatorial) coordinate system. Thus the obtained equations represent the kinematic model of the satellite rotational motion. The solution to these equations approximating the actual motion is derived from the condition of the best (in the sense of the least-square method) matching measurement data of the EMF strength vector with the calculated values. The described procedure allows us to reconstruct the actual rotational satellite motion using one solution to kinematic equations over time intervals with durations of more than 5 h. Found reconstructions were used to calculate the residual microaccelerations.

The paper considers the ballistic design of spacecraft (SC) transfer to the neighborhood of the L2 point and subsequent entry of the SC into the halo orbit. Trajectory calculations of one-impulse Earth-halo orbit transfers with and without using a lunar gravitational maneuver are presented. For the calculation of one-impulse trajectories of Earth-halo-orbit transfers, an algorithm for constructing initial approximations is applied. These approximations are constructed by calculating and analyzing the isolines as a function of two variables. This function is represented by the pericenter height of the outgoing orbit over the Earth’s surface. The arguments of the function are special parameters that characterize the halo orbit. The mentioned algorithm allows one to obtain halo orbits with specified geometrical characteristics both in the ecliptic plane, and in the plane orthogonal to it. The estimates of the characteristic velocity expenses for maintaining SC in the selected halo orbit are obtained. The described technique was used to search for working orbits of the Spectr-RG and Millimetron spacecraft. Examples of orbits obtained are presented.

Methods are proposed for constructing the orbits of spacecraft remaining for long periods of time in the vicinity of the L2 libration point in the Sun-Earth system (so-called halo orbits), and the trajectories of uncontrolled flights from low near-Earth orbits to halo orbits. Halo orbits and flight trajectories are constructed in two stages: A suitable solution to a circular restricted three-body problem is first constructed and then transformed into the solution for a restricted four-body problem in view of the real motions of the Sun, Earth, and Moon. For a halo orbit, its prototype in the first stage is a combination of a periodic Lyapunov solution in the vicinity of the L2 point and lying in the plane of large-body motion, with the solution for the linear second-order system describing small deviations of the spacecraft from this plane along the periodic solution. The desired orbit is found as the solution to the three-body problem best approximating the prototype in the mean square. The constructed orbit serves as a similar prototype in the second stage. In both stages, the approximating solution is constructed by continuation along a parameter that is the length of the approximation interval. Flight trajectories are constructed in a similar manner. The prototype orbit in the first stage is a combination of a solution lying in the plane of large-body motion and a solution for a linear second-order system describing small deviations of the spacecraft from this plane. The planar solution begins near the Earth and over time tends toward the Lyapunov solution existing in the vicinity of the L2 point. The initial conditions of both prototypes and the approximating solutions correspond to the spacecraft’s departure from a low near-Earth orbit at a given distance, perigee, and inclination.

The mode of monoaxial solar orientation of a designed artificial Earth satellite (AES), intended for microgravitational investigations, is studied. In this mode the normal line to the plane of satellite’s solar batteries is permanently directed at the Sun, the absolute angular velocity of a satellite is virtually equal to zero. The mode is implemented by means of an electromechanical system of powered flywheels or gyrodynes. The calculation of the level of microaccelerations arising on board in such a mode, was carried out by mathematical modeling of satellite motion with respect to the center of masses under an effect of gravitational and restoring aerodynamic moments, as well as of the moment produced by the gyrosystem. Two versions of a law for controlling the characteristic angular momentum of a gyrosystem are considered. The first version provides only attenuation of satellite’s perturbed motion in the vicinity of the position of rest with the required velocity. The second version restricts, in addition, the increase in the accumulated angular momentum of a gyrosystem by controlling the angle of rotation of the satellite around the normal to the light-sensitive side of the solar batteries. Both control law versions are shown to maintain the monoaxial orientation mode to a required accuracy and provide a very low level of quasistatic microaccelerations on board the satellite.

The results of studying vibration microaccelerations aboard the International Space Station are presented. The study was performed using the measurement data of the MAMS low-frequency and the SAMS high-frequency accelerometers. For the study, six intervals of measurements were selected, performed in 2005. During these intervals the station was flying in the standard orbital orientation, attitude control engines were not switched on, and the crew rested. Discrete and continuous spectra were analyzed on selected intervals. The most significant disturbances with the discrete spectrum (cyclic trends) have been found. Using the second order autoregression model, parameters of the most significant disturbances with the continuous spectrum were determined. This study was carried out as a part of the technical experiment “The ISS environment”.

We investigated periodic motions of the axis of symmetry of a model satellite of the Earth, which are similar to the motions of the longitudinal axes of the Mir orbital station in 1999–2001 and the Foton-M3 satellite in 2007. The motions of these spacecraft represented weakly disturbed regular Euler precession with the angular momentum vector of motion relative to the center of mass close to the orbital plane. The direction of this vector during the motion was not practically changed. The model satellite represents an axisymmetric gyrostat with gyrostatic moment directed along the axis of symmetry. The satellite moves in a circular orbit and undergoes the action of the gravitational torque. The motion of the axis of symmetry of this satellite relative to the absolute space is described by fourth-order differential equations with periodic coefficients. The periodic solutions to this system with special symmetry properties are constructed using analytical and numerical methods.

Feature of modern info communication systems is expeditious exchange of information that makes a problem of ensuring quality and reliability of the obtained information actual. For elimination or minimization of the destabilizing impact of noise and hindrances in such systems various methods and algorithms of preliminary information processing are widely used, in particular, procedures of digital filtration of signals and images. Procedure of creation of the nonlinear SVD filter with adaptation to local properties of an observed signal is stated. Comparative examples of filtration of hindrances in a problem of processing of images are given, efficiency of the offered method is shown. The lines of further researches are defined.

The procedure of scaling images by approximating the matrix of observed data is described. A comparative analysis of the proposed method and the known approaches to the interpolation of images is conducted. The recommendations for the use of this method are given.

Theoretical justification and information opportunities of a method of restoration of digital signals and images in the conditions of action of uncorrelated hindrances is presented. The problem of allocation of pulse hindrances by means of the singular analysis of a matrix of observed data is solved. Results of experimental modeling are given.

Quasi-static microaccelerations are estimated for a satellite specially designed to perform space experiments in the field of microgravity. Three modes of attitude motion of the spacecraft are considered: passive gravitational orientation, orbital orientation, and semi-passive gravitational orientation. In these modes the lengthwise axis of the satellite is directed along the local vertical, while solar arrays lie in the orbit plane. The second and third modes are maintained using electromechanical executive devices: flywheel engines or gyrodynes. Estimations of residual microaccelerations are performed with the help of mathematical modeling of satellite’s attitude motion under the action of gravitational and aerodynamic moments, as well as the moment produced by the gyro system. It is demonstrated that all modes ensure rather low level of quasi-static microaccelerations on the satellite and provide for a fairly narrow region of variation for the vector of residual microacceleration. The semi-passive gravitational orientation ensures also a limited proper angular momentum of the gyro system.

The results of experiments with the DAKON-M convection sensor onboard the Russian orbital segment of the International Space Station are described. A comparison of the sensor measurements with the results of calculation of the quasistatic microacceleration component at the point of installation is made. For this comparison we have used three measurement intervals of the experiments in 2009, during which spacecraft were docked with the station, undocked from it, and actuation of jet engines of the attitude control system took place. When calculating microacceleration, we use the measurement data of the low-frequency MAMS accelerometer, installed on the American segment, and the telemetry data on the ISS rotational motion. This information allowed one to convert the MAMS measurements to the point of installation of the DAKON-M convection sensor. A comparison of sensor measurements with calculated microaccelerations showed sufficiently accurate coincidence between the calculated and measured data.

Non-standard situation on a spacecraft (Earth’s satellite) is considered, when there are no measurements of the spacecraft’s angular velocity component relative to one of its body axes. Angular velocity measurements are used in controlling spacecraft’s attitude motion by means of flywheels. The arising problem is to study the operation of standard control algorithms in the absence of some necessary measurements. In this work this problem is solved for the algorithm ensuring the damping of spacecraft’s angular velocity. Such a damping is shown to be possible not for all initial conditions of motion. In the general case one of two possible final modes is realized, each described by stable steady-state solutions of the equations of motion. In one of them, the spacecraft’s angular velocity component relative to the axis, for which the measurements are absent, is nonzero. The estimates of the regions of attraction are obtained for these steady-state solutions by numerical calculations. A simple technique is suggested that allows one to eliminate the initial conditions of the angular velocity damping mode from the attraction region of an undesirable solution. Several realizations of this mode that have taken place are reconstructed. This reconstruction was carried out using approximations of telemetry values of the angular velocity components and the total angular momentum of flywheels, obtained at the non-standard situation, by solutions of the equations of spacecraft’s rotational motion.

The results of reconstruction of uncontrolled rotational motion of the Foton-12 satellite using the measurement data of onboard sensors are presented. This problem has already been solved successfully several years ago. The satellite motion was reconstructed using the data of measuring the Earth’s magnetic field. The data of measuring the angular velocity and microaccelerations by the QSAM system were actually not used for this purpose, since these data include a clearly seen additional component whose origin was at that time unclear. This component prevented one from using these data directly for reconstruction of the angular motion. Later it became clear that the additional component was caused by the Earth’s magnetic field. Discovery of this fact allowed us to make necessary corrections when processing the QSAM system data and to use them for reconstruction of rotational motion of Foton-12. Below, a modified method of processing the QSAM system data is described together with the results of its application. The main result is obtained by comparing the motion reconstructed from measurements of angular velocity or acceleration with that found by way of processing the measurements of the Earth’s magnetic field. Their coincidence turned out to be rather accurate.

Thermophysical characteristics of phenolic carbon-filled plastic P-5-13P and graphite V-1 have been investigated on an experimental setup simulating an actual solid-propellant rocket engine. Temperature and heat-flux density on the thermally stressed boundaries of samples of the materials under study have been determined by solution, with a regularizing algorithm, of the boundary inverse problem.

A new mathematical model of the uncontrolled rotational motion of the Foton satellite is presented. The model is based on the Euler dynamic equations of rigid body motion and takes into account the action upon the satellite of four external mechanical moments: gravitational, restoring aerodynamic, moment with constant components in the satellite-fixed coordinate system, and moment arising due to interaction of the Earth’s magnetic field with the satellite’s proper magnetic moment. To calculate the aerodynamic moment a special geometrical model of the outer satellite shell is used. Detailed form of the formulas giving above-mentioned moments in the equations of satellite motion is agreed with the form of the considered motion. Model testing is performed by determining with its help the rotational motion of the Foton M-2 satellite (it was in orbit from May 31, 2005 to June 16, 2005) using the data of the onboard measurements of the Earth’s magnetic field strength. The use of the new model has led to a relatively small improvement in the accuracy of the motion determination, but allowed us to obtain physically real estimates of some parameters.

Two methods of calculating the resultant vector and principal moment of light pressure forces, having an effect on a spacecraft with a composite solar sail, are compared. The first method is based on analytical formulas obtained without regard to shading of some parts of the sail by others. The second method uses a detailed geometrical model of the sail, which allows one to take such shading into account. Some part of photons falling on a sail is supposed to be reflected from it in a mirror manner, while the others are completely absorbed. The range of variation of sail orientation parameters with respect to incident solar light streams, where the first method turns out to be accurate enough, is found.

The results of investigating free oscillations of the International Space Station construction appearing during spacecraft docking and undocking are described. The study is carried out using the measurement data of the low-frequency MAMS accelerometer. Several intervals of measurements performed in 2005 and 2006 were chosen to be studied. For chosen intervals, only the data intervals corresponding to the process of free attenuation of the oscillations construction elements were analyzed. Characteristic frequencies of elastic oscillations of the station construction and attenuation coefficients corresponding to them are found. The comparative analysis of the results obtained for various docking ports (nodes) is carried out. The described study is performed as a part of the technical experiment “The ISS Environment” carried out onboard the station in accordance with the Russian program of scientific and engineering experiments.