On the controllability of regular satellite precessions in gravitational and magnetic fields

Cover Page

Cite item

Full Text

Open Access Open Access
Restricted Access Access granted
Restricted Access Subscription or Fee Access

Abstract

The controllability in problems of stabilization of regular precessions of a dynamically symmetric satellite, the center of mass of which moves in a circular orbit in the gravitational and magnetic fields of the Earth, are considered. The satellite is equipped with magnetic coils and an electrostatically charged screen. Control moments are formed due to the interaction of the satellite’s own magnetic moment and its charge with the Earth’s magnetic field. The motion equations of the satellite relative to the mass center allow for steady-state motions—regular precessions. The equations of motion linearized in the vicinity of regular precessions represent the linear time-varying differential systems due to the time dependence of the geomagnetic field induction. The controllability of the system has been studied, which is a necessary step in the correct construction of effective stabilization algorithms. A comparative analysis of the controllability conditions of systems was carried out in the case of joint use of control moments and in the case of using each type of control moments separately.

Full Text

Restricted Access

About the authors

V. I. Kalenova

Lomonosov Moscow State University

Author for correspondence.
Email: kalenova44@mail.ru
Russian Federation, Moscow

V. M. Morozov

Lomonosov Moscow State University

Email: moroz@imec.msu.ru
Russian Federation, Moscow

A. A. Tikhonov

St. Petersburg State University

Email: a.tikhonov@spbu.ru
Russian Federation, St. Petersburg

References

  1. Beletsky V.V. Motion of a Satellite about Its Center of Mass in the Gravitational Field. Moscow: MSU Pub., 1975. 308 p. (in Russian)
  2. Rumjantsev V.V. Stability of Stationary Motions of Satellites. Moscow: Vych. Center AN SSSR, 1967. 141 p. (in Russian)
  3. Chernousko F.L. On the stability of the satellite's regular precession // JAMM, 1964, vol. 28, iss. 1, pp. 155–157.
  4. Morozov V.M. On the stability of the gyrostat motion under the action of gravitational magnetic and aerodynamic moments // Cosmic Res., 1967, vol. 5, no. 5, pp. 727–732. (in Russian)
  5. Morozov V.M. On the stability of the relative equilibrium of a satellite under the action of gravitational, magnetic and aerodynamic moments // Cosmic Res., 1969, vol. 7, no. 3, pp. 395–401. (in Russian)
  6. Sarychev V.A. Dynamics of a satellite under the control of gravitational and aerodynamic moments // in: Problems of Analytical Mechanics and Stability Theory. Moscow: Fizmatlit, 2009. pp. 111–126.
  7. Mostaza-Prieto D., Roberts P.C.E. Methodology to analyze attitude stability of satellites subjected to aerodynamic torques // J. Guid. Control. Dyn., 2016, vol. 39, pp. 437–449.
  8. Ovchinnikov M.Yu., Roldugin D.S. Recent advances in the active magnetic control of satellites // Spacecraft&Technol., 2019, vol.3, no. 2 (28), pp. 73–86.
  9. Tikhonov A.A. A method of semipassive attitude stabilization of a spacecraft in the geomagnetic field // Cosmic Res., 2003, vol. 41(1), pp. 63–73.
  10. Aleksandrov A.Yu., Aleksandrova E.B., Tikhonov A.A. Stabilization of a programmed rotation mode for a satellite with electrodynamic attitude control system // Advances in Space Res., 2018, vol. 62, pp. 142–151.
  11. Kalenova V.I., Morozov V.M. Novel approach to attitude stabilization of satellite using geomagnetic Lorentz forces // Aerosp. Sci. Technol., 2020, vol. 106. https://doi.org/10.1016/j.ast.2020.106105
  12. Morozov V.M, Kalenova V.I. Linear Time-Varying Systems and Stabilization of the Satellite Motions near the Center of Mass in a Geomagnetic Field. Moscow: MSU, 2023. 174 p. (in Russian)
  13. Morozov V.M., Kalenova V.I., Rak M.G. Stabilization of stationary motions of a satellite near the center of mass in a geomagnetic field // Itogi Nauki Tekh. Ser. Sovrem. Mat., Prilozh. Tematich. Obz., 2023, vol. 220, pp. 7185; vol. 220, pp. 71–85; vol. 221, pp. 71–92; vol. 222, pp. 42–63; vol. 223, pp. 84–106; vol. 224, pp. 15–124. (in Russian)
  14. Kalenova V.I., Morozov V.M., Tikhonov A.A. The problem of satellite attitude stabilization in the geomagnetic field // Uch. Zap. Kazan. Univ. Ser. Fiz.-Matem. Nauki, 2024, vol. 166, no. 4, pp. 499–517. (in Russian)
  15. Morozov V.M., Kalenova V.I., Rak M.G. On the stabilization of the regular precessions of satellite by means of magnetic moments // Mech. of Solids, 2021, vol.56, no. 8, pp. 1486–1499.
  16. Kalenova V.I., Morozov V.M., Rak M.G. Stabilization of regular precessions of a satellite using moments of Lorentz forces // Cosmic Res., 2024, vol. 62(1), pp. 89–96.
  17. Kalenova V.I., Morozov V.M. Linear Time-Varying Systems and Their Application to the Problems of Mechanics. Moscow: Fizmatlit, 2010. 207 p. (in Russian)
  18. Kalenova V.I., Morozov V.M., Rak M.G. On methodology for solving control problems of one class of time-varying systems // Lobachevskii J. of Math. Kazan. Gos. Univ., 2023, vol. 44, no. 1, pp. 328–336.
  19. Wertz J. Spacecraft Attitude Determination and Control. Dordrecht,The Netherlands: D. Reidel Publ. Co., 1978. 858 p.
  20. Lurie A.A. Analytical Mechanics. Moscow: GIFML, 1961. 824 p. (in Russian)
  21. Sukhov E. Numerical approach for bifurcation and orbital stability analysis of periodic motions of a 2-DOF autonomous Hamiltonian system // J. Phys. Conf. Ser., 1925, 2021, 012013.21.
  22. Krasovsky N.N. Motion Control Theory. Linear Systems. Moscow: Nauka, 1968. 476 p. (in Russian)
  23. Morozov V.M, Kalenova V.I. On the application of methods of reducibility theory to some problems in the dynamics of gyroscopic systems // Izv. AN USSR. MTT, 1987, no. 1, pp. 8–14.

Supplementary files

Supplementary Files
Action
1. JATS XML
Download
2. Fig. 1. Regular precessions of the satellite: a) cylindrical precession, b) hyperboloidal precession; c) conical precession

Download (111KB)
Indexing metadata

Copyright (c) 2025 Russian Academy of Sciences