Rotational motion of <Emphasis Type="Italic">Foton M-4</Emphasis>

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.     

Study of the mode of angular velocity damping for a spacecraft at non-standard situation

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.     

Estimation of residual microaccelerations on board an artificial earth satellite in the monoaxial solar orientation mode

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.     

Realization of modes of satellite attitude motion with a small level of microaccelerations using electromechanical executive devices

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.     

Uncontrolled rotational motion of the <Emphasis Type="Italic">Aist</Emphasis> small spacecraft prototype

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.     

Estimating the accuracy of the technique of reconstructing the rotational motion of a satellite based on the measurements of its angular velocity and the magnetic field of the Earth

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°.     

Processing the data of measurements of angular velocity and microaccelerations onboard the <Emphasis Type="Italic">Foton-12</Emphasis> satellite

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.     

The Mode of Gravitational Orientation for the International Space Station

The results of the determination of the uncontrolled attitude motion of the International Space Station during its unmanned flight in 1999 are presented. The data of onboard measurements of three components of the angular velocity are used for this determination. These data covering an interval of slightly less than one orbit were jointly processed by the least squares method, by integrating the equations of motion of the station relative to its center of mass. As a result of this processing, the initial conditions of the motion and the parameters of the mathematical model used were estimated. The actual motion of the station has been determined for 20 such intervals during April–November. Throughout these intervals, the station rotated about the axis of the minimum moment of inertia, the latter executing small oscillations relative to the local vertical. Such a mode, known as the mode of gravitational orientation of a rotating satellite or the mode of generalized gravitational orientation, was planned before the flight. The measurements were made to verify it. The quasistatic component of the microaccelerations aboard the station is estimated for this mode.     

Determination of parameters of attitude motion of a small communication satellite using the data of measurements of current of solar panels

A communication satellite (small spacecraft) injected into a geosynchronous orbit is considered. Flywheel engines are used to control the rotational spacecraft motion. The spacecraft after the emergency situation has passed into a state of uncontrolled rotation. In this case, no direct telemetric information about parameters of its rotational motion was accessible. As a result, the problem arose to determine the rotational satellite motion according to the available indirect information: current taken from the solar panels. Telemetric measurements of solar panel current obtained on the time interval of a few hours were simultaneously processed by the least squares method integrating the equations of rotational satellite motion. We present the results of processing 10 intervals of the measurement data allowing one to determine the real rotational spacecraft motion and to estimate the total angular momentum of flywheel engines.     

Determination of attitude motion of the <Emphasis Type="Italic">Foton M-3</Emphasis> satellite according to the data of onboard measurements of the Earth’s magnetic field

The results of reconstruction of rotational motion of the Foton M-3 satellite during its uncontrolled flight in September 2007 are presented. The reconstruction was performed by processing the data of onboard measurements of the Earth’s magnetic field obtained by the DIMAC instruments. The measurements were carried out continuously throughout the flight, but the processing technique dealt with the data portions covering time intervals of a few orbital revolutions. The data obtained on each such interval were processed jointly by the least squares method with using integration of the equations of satellite motion relative to its center of mass. When processing, the initial conditions of motion and the used mathematical model’s parameters were estimated. The results of processing 16 data sets gave us complete information about the satellite motion. This motion, which began at a low angular velocity, had gradually accelerated and in five days became close to the regular Euler precession of an axisymmetric solid body. At the end of uncontrolled flight the angular velocity of the satellite relative to its lengthwise axis was 0.5 deg/s; the angular velocity projection onto the plane perpendicular to this axis had a magnitude of about 0.18 deg/s.     

万有引力场中带挠性太阳帆板航天器的姿态稳定性

本文讨论带双侧挠性太阳帆板航天器在万有引力场中的姿态运动，建立带挠性帆板航天器的欧拉方程和帆板强迫振动方程。利用Ｇａｌｅｒｋｉｎ方法对动力学方程离散化，利用Ｋｅｌｖｉｎ－Ｔａｉｔ－Ｃｈｅｔａｙｅｖ定量判断航天器在轨道坐标系内相对平衡的稳定性。导出适用于任意阶模态的解析形式稳定性充分条件。     

The results of flight tests of an attitude control system for the Chibis-M microsatellite

The attitude control system of the Chibis-M microsatellite is described. Results of flight experiments on damping the initial angular velocity (made using magnetorquers) are considered, as well as stabilization in the orbital referece frame, and orientation of solar arrays toward the Sun using reaction wheels. The operation of algorithms of satellite attitude determination on sunlit and shadow segments of the orbit is also under study. The general logic of operation of the attitude control system in automatic mode is presented and discussed.     

Evolution of the Orbit of an Earth Satellite with a Solar Sail

The efficiency of using the light pressure of solar radiation for increasing the semimajor axis of the orbit of an Earth Satellite carrying a solar sail is estimated. The orbit is nearly circular and has an altitude of about 900 km. The satellite is in the mode of single-axis solar orientation: it rotates at an angular velocity of 1 deg/s around the axis of symmetry, which traces the direction to the Sun. This mode is maintained by the solar sail, which serves in this case as a solar stabilizer. The following method of increasing the semimajor axis of the orbit (which is equivalent to increasing the total energy of the satellite's orbital motion) is considered. On those sections of the orbit, where the angle between the light pressure force acting upon the sail and the vector of geocentric velocity of the satellite does not exceed a specified limit, the sail is functioning as a solar stabilizer. On those sections of the orbit, where the above-indicated angle exceeds this limit, the sail is furled by way of turning the edges of the petals towards the Sun. Such a control increases the semimajor axis by more than 150 km for three months of flight. In this case, the accuracy of solar orientation decreases insignificantly.     

Single-Axis Solar Orientation of a Satellite of the Earth

The possibility of using the mode of single-axis solar orientation is considered for a satellite placed into a nearly circular orbit with an altitude of 900 km and bearing a solar sail. The satellite (together with the sail) has an axisymmetric structure, its symmetry axis being the principal central axis of the maximum moment of inertia. The center of the sail pressure lies on this axis and is displaced with respect to the satellite's center of mass. The symmetry axis of the satellite is set to the Sun so that its center of mass would be located between the Sun and the pressure center and would rotate around this axis with an angular velocity of a few degrees per second. The satellite's axis of symmetry makes a slow precession under the action of the gravitational moment and the moment of light pressure forces. Though the maximum magnitudes of these moments are comparable, the moment of the light pressure forces dominates and controls the precession in such a way that the symmetry axis orientation to the Sun remains unchanged.     

Analysis of the orbital motion of the asteroid Apophis’ satellite

We have analyzed the orbital disturbed spacecraft motion near an asteroid. The equations of the asteroidocentric spacecraft motion have been used with regard to three perturbations from celestial bodies, the asteroid’s nonsphericity, and solar radiation pressure. It has been shown that the orbital parameters of the main spacecraft and a small satellite with a radio beacon can be selected such that the orbits are rather stable for a fairly long period of time, i.e., a few weeks for the main spacecraft with an orbit initial radius of ~0.5 km and a few years before approaching Apophis with the Earth in 2029, for a small satellite at an orbit initial radius of ~1.5 km. The initial orientation of the spacecraft orbital plane perpendicular to the sunward direction is optimal from the point of view of the stability of the spacecraft flight near an asteroid.     

目标捕获后航天器组合体的角动量转移与抑振规划

针对失稳目标捕获后航天器组合体的位姿调整与稳定问题，提出一种组合体角动量转移与振动抑制复合规划方法。首先建立了同时考虑了空间机械臂、目标卫星太阳翼、服务卫星太阳翼等柔性构件的航天器组合体动力学模型。然后提出角动量转移优化方法，规划机械臂最终构型，保证组合体相对稳定后的角速度最小；基于粒子群算法设计了机械臂最优抑振轨迹规划方法，抑制角动量转移过程中的机械臂和太阳翼的柔性振动。最后通过数值仿真验证了规划方法的有效性。仿真结果表明，该方法能够有效实现组合体的角动量转移，并显著降低组合体的柔性振动，具有工程实用性。     

Uncontrolled motion of the <Emphasis Type="Italic">Foton M-2</Emphasis> satellite and quasistatic microaccelerations on its board

The results of determining the uncontrolled rotational motion of the Foton M-2 satellite (in orbit from May 31 to June 16, 2005) are presented. The determination was made using the data of onboard measurements of the Earth’s magnetic field strength. Segments 270 min long (three orbits) were selected from these data covering the first two thirds of the flight. On each such segment the data were processed jointly by the least squares method using integration of the equations of attitude motion of the satellite. In processing, the initial conditions of motion and parameters of the used mathematical model were estimated. The thus obtained results gave a complete overview of the satellite motion. This motion, having started with a small angular velocity, gradually accelerated, and in two days became close to the regular Euler precession of an axisymmetric solid body. On June 09, 2005 (the last day of measurements) the angular velocity of the satellite relative to its lengthwise axis was about 1.1 deg/s, while the projection of the angular velocity onto a plane perpendicular to this axis had an absolute value of about 0.11 deg/s. Deviations of the lengthwise axis from a normal to the orbit plane did not exceed 60°. Based on the results of determination of the rotational motion of the satellite, calculations of quasi-static microaccelerations on its board are performed.     

An Analysis of the Low-Frequency Component in Measurements of Angular Velocity and Microacceleration onboard the Foton-12 Satellite

We compare the results of two methods used to determine the angular velocity of the Foton-12 satellite and the low-frequency component of microaccelerations onboard it. The first method is based on reconstruction of the satellite's rotational motion using the data of onboard measurements of the strength of the Earth's magnetic field. The motion (time dependence of the orientation parameters and angular velocity) was found from the condition of best approximation of the measurement data by the functions calculated along the solutions to equations of attitude motion of the satellite. The solutions found were used to calculate the quasistatic component of microaccelerations at certain points of the satellite, in particular, at the point of location of an accelerometer of the QSAM system. Filtration of the low-frequency component of the angular velocity and microacceleration from the data of measurements by a sensor of angular velocity and by the accelerometer of this system served as a second method. The filtration was made using the discrete Fourier series. A spectral analysis of the functions representing the results of determining the angular velocity and microacceleration by both methods is performed. Comparing the frequencies and amplitudes of the harmonic component of these functions allowed us to estimate the accuracy of measurements made by the QSAM system in the low-frequency range.     

Determination of parameters of rotational motion of the <Emphasis Type="Italic">Monitor-E</Emphasis> spacecraft from the telemetry data on solar batteries’ current

The Monitor-E spacecraft executed uncontrolled flight due to emergency situation, no telemetry information on parameters of the spacecraft’s attitude motion being available. So, the problem arose to determine the spacecraft’s rotational motion from the accessible indirect information—the electric current provided by solar batteries. In this paper the integrated statistical technique is described, that allows one to solve this problem. The values of current, obtained over the time interval some tens of minutes long, have been processed simultaneously by the least squares method using the integration of the equations of spacecraft’s rotational motion. As a result of processing, the initial conditions of motion were estimated, and the spacecraft’s moments of inertia were updated, as well as the angles, specifying solar batteries position in the spacecraft-fixed coordinate system. The results of processing of 12 data sets are presented, which allowed us to reconstruct the actual rotational motion of the spacecraft.     

Experimental investigation of the modes of operation of uncontrolled attitude motion of the Progress spacecraft

Results of in-flight tests of three modes of uncontrolled attitude motion of the Progress spacecraft are described. These proposed modes of experiments related to microgravity are as follows: (1) triaxial gravitational orientation, (2) gravitational orientation of the rotating satellite, and (3) spin-up in the plane of the orbit around the axis of the maximum moment of inertia. The tests were carried out from May 24 to June 1, 2004 onboard the spacecraft Progress M1-11. The actual motion of this spacecraft with respect to its center of mass, in the above-mentioned modes, was determined by telemetric information about an electric current tapped off from solar batteries. The values of the current obtained during a time interval of several hours were processed jointly using the least squares method by integration of the equations of the spacecraft’s attitude motion. The processing resulted in estimation of the initial conditions of motion and of the parameters of mathematical models used. For the obtained motions the quasi-static component of microaccelerations was computed at a point onboard, where installation of experimental equipment is possible.