Passive Magnetic Attitude Control System for the Munin Nanosatellite

The instrumental and applied problems related to the design of a passive magnetic attitude control system for the Munin nanosatellite are considered. The system is constructed from a strong permanent magnet and a set of hysteresis rods. These rods are made of magnetically soft material using a special technology, and they allow us to support the satellite orientation with respect to the local magnetic field vector with a given accuracy and time response. By using asymptotic and numerical methods, we investigate the satellite dynamics for different models of hysteresis. The issues concerning the arrangement of the rods and their interaction with the fields of permanent magnets mounted onboard the satellite are discussed.     

Nanosatellite <Emphasis Type="Italic">REFLECTOR</Emphasis>: Choice of parameters of the attitude control system

We consider methodological and applied problems of choosing parameters and developing a passive gravity-gradient attitude control system for the REFLECTOR nanosatellite. The attitude control system consists of appropriately distributed satellite mass and additional masses forming the required tensor of inertia, as well as of a set of hysteresis rods manufactured from a magnetically soft material. The combination of these elements allows one, independent of the satellite’s initial angular motion, to maintain its three-axial orientation in the orbital coordinate system with preset performance in precision and fast response. The satellite’s dynamics is investigated using asymptotic and numerical methods. The problems of arrangement of the additional masses and hysteresis rods are discussed, as well as their interaction with magnetizable elements.     

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.     

Determination of <Emphasis Type="Italic">Foton M-2</Emphasis> satellite attitude motion by the data of microacceleration measurements

The results of reconstruction of uncontrolled attitude motion of the Foton M-2 satellite using measurements with the accelerometer TAS-3 are presented. The attitude motion of this satellite has been previously determined by the measurement data of the Earth’s magnetic field and the angular velocity. The TAS-3 data for this purpose are used for the first time. These data contain a well-pronounced additional component which made impossible their direct employment for the reconstruction of the attitude motion and whose origin was unknown several years ago. Later it has become known that the additional component is caused by the influence of the Earth’s magnetic field. The disclosure of this fact allowed us to take into account a necessary correction in processing of TAS-3 data and to use them for the reconstruction of the attitude motion of Foton M-2. Here, a modified method of processing TAS-3 data is described, as well as results of its testing and employing. The testing consisted in the direct comparison of the motion reconstructed by the new method with the motion constructed by the magnetic measurements. The new method allowed us to find the actual motion of Foton M-2 in the period June 9, 2005–June 14, 2005, when no magnetic measurements were carried out.     

The use of refined model of aerodynamic moment in the problem of reconstruction of the <Emphasis Type="Italic">Foton</Emphasis> satellite rotational motion

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.     

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.     

Single-impulse transfers from orbits of artificial satellites to orbits around <Emphasis Type="Italic">L</Emphasis><Subscript>1</Subscript> or <Emphasis Type="Italic">L</Emphasis><Subscript>2</Subscript> libration points

In the context of the restricted circular three-body problem a method for constructing families of periodic orbits is described. Each orbit contains a segment of transfer from artificial satellite orbit of a smaller body to an orbit around L ₁ or L ₂ points of the Sun-Earth and Earth-Moon systems, a segment of multiple flyby of this libration point, and a segment of return to the artificial satellite orbit. Dependences of velocities at the pericenter on the pericenter radius are given.     

An analysis of low-frequency component in microacceleration measurements made onboard the <Emphasis Type="Italic">Foton M-2</Emphasis> satellite

The low-frequency component is investigated in the data of measurements performed onboard the Foton M-2 satellite with the three-component accelerometer TAS-3. Investigations consisted in comparison of this component with its calculated analog found from a reconstruction of the satellite’s attitude motion. The influence of the Earth’s magnetic field on the accelerometer readings is discovered by way of spectral analysis of the functions representing the results of determining the low-frequency microacceleration by two methods. After making correction for this influence, the results obtained by these two methods coincided within a root-mean-square error of less than 10^?6 m/s².     

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.     

Characteristics of thermal ion outflows in the polar cap according to data of the <Emphasis Type="Italic">Interball-2</Emphasis> satellite

Characteristics of polar wind fluxes at a height of ∼20000 km measured by the Hyperboloid mass-spectrometer installed onboard the Interball-2 satellite are presented in the paper. The characteristics are presented for the upwelling flows of ionospheric ions H⁺, He⁺, and O⁺ from the sunlit polar cap in the period of solar activity minimum. Orbit segments with minimal precipitation of magnetospheric ions and electrons were preliminarily selected, and the measurements where the fluxes of ions coming from the cusp/cleft were excluded as carefully as possible. Thus, the densities, field-aligned velocities, and temperatures of ions in the regions where fluxes of polar wind could be detected with the maximal probability degree are presented in the paper. It is found that cases when only H⁺ ions are reaching the detector are with high probability the polar wind outflows. Their characteristics agree well with the Tube-7 hydrodynamic model and are as follows: n ≈ 1.5 cm⁻³, V _∥ ∼ 21 km/s; T _∥ = 3500 K, and T _⊥ = 2000 K. In cases when He⁺ and O⁺ ions are also detected, the temperatures are substantially higher than the model ones, and the measured field-aligned velocities of O⁺ fluxes are several times higher than the model ones. Moreover, it was revealed that the polar wind outflows are predominantly observed in the polar cap regions where the polar rain fluxes are very small.     

Observations of auroral kilometric radio emission on the <Emphasis Type="Italic">Interball-1</Emphasis> satellite in the active Sun period 1999–2000

Results of almost two years (January 1999–October 2000) of continuous observations of auroral kilometric radio emission with the instrument AKR-X onboard the high-apogee satellite of the Earth Interball-1 are presented. The observations were conducted at the growth stage (in 1999) and in the maximum (2000) of solar activity within the 100–1500 kHz frequency band. The results of AKR detection in the vicinity of the maximum of its spectrum at a frequency of 252 kHz are presented. Both similarity (for example, the character of global directivity) and important differences from the AKR emission observed during the solar activity minimum [5] are found. Together with very high sporadicity, strong seasonal changes in the intensity are typical for the emission. It is completely absent in the spring-summer period in the Northern Hemisphere and is strongly suppressed in this period in the Southern Hemisphere. Probable nature of these features of AKR is discussed.     

用地球磁场和重力场成功挽救风云一号（B）卫星的控制技术

风云一号气象卫星是我国最早成功发射的太阳同步三轴稳定对地遥感卫星，由于早期的技术和器件原因，星上计算机因空间辐照而失控，造成星上贮气耗尽、卫星高速翻滚。本文详细介绍了了在卫星面临失败的情况下，作者利用地球磁场和重力场与卫星的相互作用，采用星上的磁力矩器和可用的一切手段而设计的一整套抢救这颗卫星的技术方法，并简述了经过75天的艰苦努力，使这颗濒临失败的卫星重新建立三轴稳定的对地定向姿态的历程。     

CRYOGENIC TECHNOLOGY TO IMPROVE ELECTRIC THRUSTERS

This paper analyzes superconducting (SC) coils technology to improve satellite electric propulsion. SC magnets can generate very high magnetic fields with extremely low ohmic losses, low electric power and PCU weight. Moreover, the weight of SC magnet coils is quite low compared with conventional or permanent magnets capable of producing the same field strength. For instance, to obtain a 0.4 T magnetic field strength, typical of applied field magnetoplasmadynamic thrusters (AF-MPD), based on the Lorentz force, and with thrust in the range of 1 N, this paper shows that only a 40 g coil SC weight is needed, whereas an equivalent field copper winding would weigh about 36 kg. Using SC technology it is shown that the limited magnetic induction provided by a permanent magnet may be raised and also that it is possible to obtain high magnetic fields (of order of several Tesla) with fewer turns, drastically reducing coil volume, weight and complexity compared to conventional winding.

Superconductivity at low temperature (LTSC) requires liquid helium at 4.2 K to produce very high current densities: the thermal analysis in this paper shows that, depending on satellite and thruster, high temperature superconductors (HTSC) wires are sometimes better than LTSC because these can support lower current densities but with a critical superconductivity temperature higher than for LHe, requiring LN₂ at 77 K, easier to maintain during the whole mission.

Finally, this paper shows that implementing SC cryogenic technology on a satellite can be achieved with current active coolers technology.     

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.     

Space-time structure of ion-cyclotron waves in the topside ionosphere as observed onboard the <Emphasis Type="Italic">ST</Emphasis>-<Emphasis Type="Italic">5</Emphasis> satellites

Results of observations of ion-cyclotron (IC) waves onboard the ST-5 satellites in the topside ionosphere (heights from a few hundred up to thousands of km) are presented. In this project, three identical micro-satellites were located during three months in 2006 in almost identical orbits with distances between them from first thousands to hundreds of km. All ion-cyclotron wave packets detected by two-three probes were observed at crossing one and the same latitude, which manifests their narrow localization in latitude with a characteristic scale from the first tens to 100 km. In no event IC waves were recorded with comparable amplitudes by all three satellites. At the same time, in the case of ST-5 flight near the ground-based induction magnetometer, a long emission in the same frequency range on the ground corresponded to a burst of IC waves in the topside ionosphere. This can indicate to the fact that an IC instability develops not continuously, but in the pulsing regime with a characteristic time of up to ∼10 min. A change in the rotation direction when a satellite crosses the wave structure is a characteristic feature of the polarization structure of registered transverse waves. The detected effects are discussed from the point of view of the existing models of generation and waveguide propagation of IC waves.     

基于重力梯度杆和磁铁的小卫星三轴姿态控制

运用卫星低轨道两个主要环境力矩（重力梯度矩和地磁力矩）对圆轨道卫星三轴姿态进行被动控制。利用重力梯度矩实现卫星对地指向：卫星上的永久磁铁获取所需的地磁力矩,稳定偏航姿态。给出卫星的姿态分析,并给出仿真结果。从分析和仿真结果可以看出,此卫星具有结构简单、时刻对地定向、低轨道倾角时卫星姿态稳定精度较高的优点。     

Design of satellite constellations with continuous coverage on elliptic orbits of <Emphasis Type="Italic">Molniya</Emphasis> type

New methods of choosing the structures of satellite constellations (SC) on elliptical orbits of the Molniya type are presented. The methods, using critical inclination and putting the orbit apogee in the Earth’s hemisphere with an area of continuous coverage, are based on geometrical analysis of two-dimensional representation of the coverage conditions and SC motion in the space of inertial longitude of the orbit ascending node and time. The coverage conditions are represented in the form of a certain region. Dynamics of all satellites in this space is represented by uniform motion along a straight line approximately parallel to the ordinate axis, while the satellite system forms a grid. The problem of choosing a minimal (as far as the number of satellites is concerned) SC configuration can be formulated as a search for the most sparse grid. The contemporary advanced methods of computational geometry serve as an algorithmic basis for the problem solution. Design of SC for continuous coverage of latitude belts with the use of kinematically regular systems is considered. A method of analyzing single-track systems for continuous coverage of arbitrary geographic regions is described, which makes a region at any time instant observable by at least one satellite of the system. As an example, SC on elliptical orbits are considered with periods of ～4, 12, and 24 hours.     

Determination of the Attitude Motion of a Satellite Based on a Kinematical Model of Motion and Using Data of Measurements of Its Angular Velocity and the Earth’s Magnetic Field Strength

An integral statistical procedure of determination of the attitude motion of a satellite using the data of onboard measurements of angular velocity vectors and the strength of the Earth’s magnetic field (EMF) is suggested. The procedure uses only the equations of kinematics of a solid body and is applicable to determining both controlled and uncontrollable motions of a satellite at any external mechanical moments acting upon it. When applying this procedure, the data of measurements of both types, accumulated during a certain interval of time, are processed jointly. The data of measuring the angular velocity are smoothed by discrete Fourier series, and these series are substituted into kinematical Poisson equations for elements of the matrix of transition from a satellite-fixed coordinate system to the orbital coordinate system. The equations thus obtained represent a kinematical model of the satellite motion. The solution to these equations (which approximate the actual motion of a satellite) is found from the condition of the best (in the sense of the least squares method) fit of the data of measuring the EMF strength vector to its calculated values. The results of testing the suggested procedure using the data of measurements of the angular velocity vectors onboard the Foton-12 satellite and measurements of EMF strengths are presented.__________Translated from Kosmicheskie Issledovaniya, Vol. 43, No. 4, 2005, pp. 295–305.Original Russian Text Copyright © 2005 by Abrashkin, Volkov, Voronov, Egorov, Kazakova, Pankratov, Sazonov, Semkin.     

反作用飞轮电机换相力矩波动抑制协同控制方法

针对反作用飞轮电机换相所产生的非理想力矩影响卫星姿态控制精度的问题,采用永磁无刷直流电机绕组感生电势、相电流和电磁转矩的解析计算方法得到了反作用飞轮电机的换相力矩波动最小化条件,提出了基于该最小化条件的换相力矩波动抑制高动态协同控制方法,抑制反作用飞轮电机三种运行状态下的换相力矩波动.试验结果表明,电动状态下换相力矩波动减小了12%、可控能耗制动和反接制动状态下换相力矩波动减小了90%以上,验证了该方法的可行性和有效性.     

Observations of the auroral hectometric radio emission onboard the <Emphasis Type="Italic">INTERBALL-1</Emphasis> satellite

The results of five-year (1995–2000) continuous observations of the auroral radio emission (ARE) in the hectometric wavelength range on the high-apogee INTERBALL-1 satellite are presented. Short intense bursts of the auroral hectometric radio emission (AHR) were observed at frequencies of 1463 and 1501 kHz. The bursts were observed predominantly at times when the terrestrial magnetosphere was undisturbed (in the quiet Sun period), and their number decreased rapidly with increasing solar activity. The bursts demonstrated seasonal dependence in the Northern and Southern hemispheres (dominating in the autumn-winter period). Their appearance probably depends on the observation time (UT). A qualitative explanation of the AHR peculiarities is given.