Steady-State Oscillations of a Satellite with Passive Attitude Control System in the Magneto-Lorentz Coordinate System

Document Type : Research Paper

Authors
Saint Petersburg State University, 7-9 Universitetskaya nab., Saint Petersburg, 199034, Russia
Abstract
In this paper, an artificial Earth satellite with an electrodynamic attitude control system is considered. Satellite attitude stabilization in the magneto-Lorentz coordinate system is studied. The problem of the analytical construction of the periodic steady-state oscillations of the satellite in the passive control mode is solved. The solution is obtained in the form of a partial sum of trigonometric series. The algorithm for constructing solution is based on the introduction of auxiliary complex variables that make it possible to transform the initial non-autonomous differential equation of the 6th order to an autonomous differential system of the 8th order, for which the procedure for analytically finding the coefficients of a trigonometric series does not present fundamental difficulties, since it is reduced to sequential transformations using recurrent formulas. The constructed steady-state oscillations of the satellite make it possible to correct measurements of on-board instruments and increase the accuracy of information transmitted from the satellite.
Keywords
Subjects

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[1] Gorr, G.V., Belokon, T.V., On solutions of the equations of motion of a gyrostat with a variable gyrostatic moment, Mechanics of Solids, 56(7), 2021, 1157–1166.
[2] Amer, T.S., Alanazy, A., Elneklawy, A.H., Amer, W.S., El-Kafly, H.F., A novel study on the fourth first integral for the rotatory motion of an impacted charged rigid body by external torques, Journal of Low Frequency Noise, Vibration and Active Control, 2025, https://doi.org/10.1177/ 14613484251347080.
[3] Kosov, A.A., On the stability of stationary solutions of the equations of motion of the Goryachev-Sretensky gyrostat, Mechanics of Solids, 58, 2023, 1986–1997.
[4] Amer, T.S., Alanazy, A., Elneklawy, A.H., Amer, W.S., El-Kafly, H.F., Asymptotic solutions for the 3D motion of asymmetric charged gyrostatic satellite using Poincare small parameter technique, Aerospace Science and Technology, 168, 2026, 110764.
[5] Sarychev, V.A., Issues of orientation for artificial satellites, Itogi Nauki Tekh., Ser.: Issled. Kosm. Prostr, vol. 11, 1978, (In Russian). 
[6] Beletsky, V.V., Yanshin, A.M., The Influence of Aerodynamics Forces on Spacecraft Rotation, Naukova Dumka, Kiev, 1984, (In Russian).
[7] Barinova, E.V., Belokonov, I.V., Timbai, I.A., Technology for designing the angular motion of cubesat nanosatellites with a passive stabilization system, Gyroscopy and Navigation, 15(4), 2024, 346-355.
[8] Wertz, J.R., Spacecraft Attitude Determination and Control, D. Reidel Publishing Co., Dordrecht, 1985.
[9] Somov Ye., Butyrin S., Somov S., Spatial guidance and control of a space robot during flights in a low-orbit constellation of Earth observation mini-satellites, Cybernetics and Physics, 13(1), 2024, 77-81.
[10] Aleksandrov, A.Yu., Antipov, K.A., Platonov, A.V., Tikhonov, A.A., Electrodynamic attitude stabilization of a satellite in the Konig frame, Nonlinear Dynamics, 82, 2015, 1493-1505. 
[11] Laundal, K.M., Richmond, A.D., Magnetic Coordinate Systems, Space Science Reviews, 206, 2017, 27-59.
[12] Beletsky, V.V., Khentov, A.A., Magnetized Spacecraft Attitude Motion. Nauka, Moscow, 1985, (In Russian).
[13] Zhou, K., Huang, H., Wang, X., Sun, L., Zhong, R., Magnetic attitude control for Earth-pointing satellites in the presence of gravity gradient, Aerospace Science and Technology, 60, 2017, 115-123.
[14] Roldugin, D.S., Extensive numerical simulation of a magnetically actuated satellite rotation around the sun direction with sun sensors data only, Mathematical Models and Computer Simulations, 15(5), 2023, 792-801.
[15] Ovchinnikov, M.Y., Roldugin, D.S., A survey on active magnetic attitude control algorithms for small satellites, Progress in Aerospace Sciences, 109, 2019, 100546.
[16] Morozov, V.M., Kalenova, V.I., Satellite Control Using Magnetic Moments: Controllability and Stabilization Algorithms, Cosmic Research, 58, 2020, 158-166.
[17] Tikhonov, A.A., A method of semipassive attitude stabilization of a spacecraft in the geomagnetic field, Cosmic Research, 41(1), 2003, 63-73.
[18] Giri, D.K., Sinha, M., Magneto-Coulombic attitude control of Earth-pointing satellites, Journal of Guidance, Control, and Dynamics, 37(6), 2014, 1946-1960.
[19] Giri, D.K., Sinha, M., Three-axis attitude control of Earth-pointing isoinertial magneto-Coulombic satellites, International Journal of Dynamics and Control, 5(3), 2017, 644-652.
[20] Prabhat, H., Mukherjee, B.K., Giri, D.K., Sinha, M., Fault-tolerant sliding mode satellite attitude stabilization using magneto-coulombic torquers, Aerospace Science and Technology, 121, 2022, 107316.
[21] 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.
[22] Tikhonov, A.A., Spasic, D.T., Antipov, K.A., Sablina, M.V., Optimizing the electrodynamical stabilization method for a man-made Earth satellite, Automation and Remote Control, 72(9), 2011, 1898-1905.
[23] Klyushin, M.A., Maksimenko, M.V., Tikhonov, A.A., Electrodynamic attitude stabilization of a spacecraft in an elliptical orbit, Aerospace, 11, 2024, 956.
[24] Tikhonov, A.A., Natural Magneto-velocity Coordinate System for Satellite Attitude Stabilization: The Concept and Kinematic Analysis, Journal of Applied and Computational Mechanics, 7(4), 2021, 2113-2119.
[25] Aleksandrov, A.Yu., Tikhonov, A.A., Natural Magneto-velocity Coordinate System for Satellite Attitude Stabilization: Dynamics and Stability Analysis, Journal of Applied and Computational Mechanics, 9(2), 2023, 513-520.
[26] Melnikov, G.I., Tikhonov, A.A., Way of Defining Periodic Movements of Nonautonomous Automatic Systems, Automation and Remote Control, 7, 1970, 5–14.