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.     

Energy measurements of electrons and protons in cosmic ray physics using satellite and balloon calorimeters in recent two decades

Calorimeters are used in cosmic ray studies for a variety of purposes, such as measurements of particle energy, separation of electrons and hadrons, formation of triggers (signals for activation of instruments), and so on. In this review we consider the methods of energy reconstruct of protons and electrons (for particles with energies exceeding 10 GeV) in calorimeters of various types that are used in astrophysical experiments of cosmic ray studies carried out with balloons and satellites.     

Numerical Simulation of Geomagnetic Trapping of Anomalous Cosmic Ray Ions

A method for simulating the propagation processes for ions of the anomalous component of cosmic rays in the Earth's magnetic field is described with allowance made for a step-by-step stripping of the ions in the residual atmosphere and their trapping by the geomagnetic field. Numerical results are presented for the geomagnetic trapping of high-energy singly charged oxygen ions penetrating into the stripping region from interplanetary space.     

Synthesis of a combined system for precise stabilization of the Spektr-UF observatory: II

The paper presents the second part of the results of search studies for the development of a combined system of high-precision stabilization of the optical telescope for the designed Spectr-UF international observatory [1]. A new modification of the strict method of the synthesis of nonlinear discrete-continuous stabilization systems with uncertainties is described, which is based on the minimization of the guaranteed accuracy estimate calculated using vector Lyapunov functions. Using this method, the synthesis of the feedback parameters in the mode of precise inertial stabilization of the optical telescope axis is performed taking the design nonrigidity, quantization of signals over time and level, and errors of orientation meters, as well as the errors and limitation of control moments of executive engine-flywheels into account. The results of numerical experiments that demonstrate the quality of the synthesized system are presented.     

A simplified technique for determining the rotational motion of a satellite based on the onboard measurements of the angular velocity and magnetic field of the Earth

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.     

Uncontrolled Attitude Motion of the Foton-12 Satellite and Quasi-Steady Microaccelerations onboard It

The results of determination of the uncontrolled attitude motion of the Foton-12 satellite (placed in orbit on September 9, 1999, terminated its flight on September 24, 1999) are presented. The determination was carried out by the onboard measurement data of the Earth's magnetic field strength vector. Intervals with a duration of several hours were selected from data covering almost the entire flight. On each such interval the data were processed simultaneously using the least squares method by integrating the satellite's equations of motion with respect to the center of mass. The initial conditions of motion and the parameters of the mathematical model employed were estimated in processing. The results obtained provided for a complete representation of the satellite's motion during the flight. This motion, beginning with a small angular velocity, gradually sped up. The growth of the component of the angular velocity with respect to the longitudinal axis of the satellite was particularly strong. During the first several days of the flight this component increased virtually after every passage through the orbit's perigee. As the satellite's angular velocity increased, its motion became more and more similar to the regular Euler precession of an axisymmetric rigid body. In the last several days of flight the satellite's angular velocity with respect to its longitudinal axis was about 1 deg/s and the projection of the angular velocity onto the plane perpendicular to this axis had a magnitude of approximately 0.15 deg/s. The deviation of the longitudinal axis from the normal to the orbit plane did not exceed 60°. The knowledge of the attitude motion of the satellite allowed us to determine the quasi-steady microacceleration component onboard it at the locations of the technological and scientific equipment.     

Synthesis of a combined system for precise stabilization of the Spektr UF observatory. I

The paper presents the first part of results of basic research for development of a combined system of high-precision stabilization of the optical telescope for the international observatory Speckr UF (currently under design) planned to study emission of stars in the UV waveband. A new direct method used in these studies for calculating program controls is described. The results of numerical experiments are presented.     

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.     

Detector of Micrometeoroid and Artificial Space Debris Particles

The mathematical model of a space debris detector based on inflatable metal-dielectric-metal (MDM) film structure is presented. The efficiency of its implementation for detection of space debris particles at different altitudes is estimated, and the information obtained by the detector is investigated.