Natural Magneto-velocity Coordinate System for Satellite ‎Attitude Stabilization: The Concept and Kinematic Analysis

Document Type : Research Paper


1 Department of Theoretical and Applied Mechanics, Saint Petersburg State University, 7-9 Universitetskaya nab., Saint Petersburg, 199034, Russia

2 Department of Mechanics, Saint Petersburg Mining University, 2, 21st Line, St. Petersburg, 199106, Russia


An artificial Earth satellite with an electric charge and an intrinsic magnetic moment is considered. Due to the geomagnetic field, the satellite experiences the influence of the Lorentz and magnetic torques. To set the angular position of the satellite, we introduce natural coordinate system associated with the directions of geomagnetic induction vector and Lorentz force vector which is orthogonal both to the geomagnetic induction and relative velocity of the satellite. It is shown that such a natural magneto-velocity coordinate system is convenient for attitude stabilization of a satellite operating in the mode of scanning the Earth's surface. The properties of the trajectory of the satellite axis on the Earth's surface are analysed. The rotation tensor connecting the natural magneto-velocity and the orbital coordinate systems is obtained. The angular velocity of the natural magneto-velocity trihedron is found. Kinematic differential equations for the unit vectors of the natural magneto-velocity coordinate system are derived.


Main Subjects

Publisher’s Note Shahid Chamran University of Ahvaz remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

[1] Petrov, K.G., Tikhonov, A.A., The moment of Lorentz forces acting on a charged satellite in the Earth's magnetic field,Vestnik Sankt-Peterburgskogo Universiteta. Ser 1. Matematika Mekhanika Astronomiya, 1, 1999, 92-100.
[2] Beletsky, V.V., Motion of an Artificial Satellite about its Center of Mass, Israel Program for Scientific Translation, Jerusalem, 1966.
[3] Battagliere, M.L., Santoni, F., Piergentili, F., Ovchinnikov, M., Graziani, F., Passive magnetic attitude stabilization system of the EduSAT microsatellite, Proc. Inst. Mech. Eng., G J. Aerosp. Eng., 224(10), 2010, 1097-1106.
[4] Krasil’nikov, P., Fast non-resonance rotations of spacecraft in restricted three body problem with magnetic torques, International Journal of Non-Linear Mechanics, 73(4), 2015, 43-50.
[5] Antipov, K.A., Tikhonov, A.A. Parametric control in the problem of spacecraft stabilization in the geomagnetic field, Automation and Remote Control, 68(8), 2007, 1333-1345.
[6] Aleksandrov, A.Yu., Antipov, K.A., Platonov, A.V., Tikhonov, A.A., Electrodynamic stabilization of artificial earth satellites in the König coordinate system, Journal of Computer and Systems Sciences International, 55(2), 2016, 296-309.
[7] Aleksandrov, A.Yu., Tikhonov, A.A., Asymptotic stability of a satellite with electrodynamic attitude control in the orbital frame, Acta Astronautica, 139, 2017, 122-129.
[8] 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 Research, 62(1), 2018, 142-151.
[9] Kalenova, V.I., Morozov, V.M., Novel approach to attitude stabilization of satellite using geomagnetic Lorentz forces, Aerospace Science and Technology, 106, 2020, 106105.
[10] Ebrahimi, F., Barati, M.R., A nonlocal higher-order refined magneto-electro-viscoelastic beam model for dynamic analysis of smart nanostructures, International Journal of Engineering Science, 107, 2016, 183-196.
[11] Shirbani, M.M., Shishesaz, M., Hajnayeb, A., Sedighi, H.M., Coupled magneto-electro-mechanical lumped parameter model for a novel vibration-based magneto-electro-elastic energy harvesting systems, Physica E: Low-Dimensional Systems and Nanostructures, 90, 2017, 158-169.
[12] Sedighi, H.M., Koochi, A., Keivani, M., Abadyan, M., Microstructure-dependent dynamic behavior of torsional nano-varactor, Measurement, 111, 2017, 114-121.
[13] Alekseev, V. V., Emel’yanov, A. P., Kozyaruk, A. E., Analysis of the dynamic performance of a variable-frequency induction motor drive using various control structures and algorithms, Russian Electrical Engineering, 87(4), 2016, 181-188.
[14] Belsky, A.A., Skamyin, A.N., Iakovleva, E.V., Configuration of a standalone hybrid wind-diesel photoelectric unit for guaranteed power supply for mineral resource industry facilities, International Journal of Applied Engineering Research, 11(1), 2016, 233-238.
[15] Dosaev, M.Z., Klimina, L.A., Lokshin, B.Y., Selyutskiy, Y.D., Shalimova, E.S. Autorotation modes of double-rotor Darrieus wind turbine, Mechanics of Solids, 56(2), 2021, 250-262.
[16] Koenigius, S., De universali principio aequilibrii et motus, in vi viva reperto, deque nexu inter vim vivam et actionem, utriusque minimo, dissertation, Nova Acta Eruditorum, 1751, 125-135, 162-176.
[17] Tikhonov, A.A., Petrov, K.G., Multipole models of the Earth's magnetic field, Cosmic Research, 40(3), 2002, 203-212.
[18] Antipov, K.A., Tikhonov, A.A., Multipole models of the geomagnetic field: Construction of the N-th approximation, Geomagnetism and Aeronomy 53(2), 2013, 257-267.
[19] Ovchinnikov, M.Y., Penkov, V.I., Roldugin, D.S., Pichuzhkina, A.V., Geomagnetic field models for satellite angular motion studies, Acta Astronautica, 144, 2018, 171-180.