Stabilization of stationary motions of a satellite near the center of mass in a~geomagnetic field. I

V. M. Morozov ; V. I. Kalenova ; M. G. Rak

Itogi nauki i tehniki. Sovremennaâ matematika i eë priloženiâ. Tematičeskie obzory, Proceedings of the International Conference «Classical and Modern Geometry» dedicated to the 100th anniversary of the birth of Professor Levon Sergeyevich Atanasyan (July 15, 1921—July 5, 1998). Moscow, November 1–4, 2021. Part 1, Tome 220 (2023), pp. 71-85

Résumé

In this paper, we consider problems of stabilization of stationary motions (equilibrium positions and regular precessions) of a satellite near the center of mass in gravitational and magnetic fields under the assumption that the center of mass moves in a circular orbit. Mathematical models of the problems considered are systems of differential equations with periodic coefficients. We present a rigorous analytical approach to this problem, which allows efficient and correct construction of stabilization algorithms. The method is based on the reducibility of nonstationary systems that describe these problems to stationary systems. Solutions for a number of problems of stabilizing stationary motions of a satellite with the help of magnetic systems are proposed. We present the results of mathematical modeling of the algorithms, which confirm the effectiveness of the developed methodology. The work is published with a continuation.

Détail

Keywords: linear nonstationary system, reducibility, stationary motions, linearized equations of satellite motions, stabilization, controllability, control algorithms.