Abstract
This paper considers the motion of a low-orbit electrodynamic tether system designed to raise the orbit of a small spacecraft or nanosatellites. The system operates in the thrust generation mode. The orbit is raised by the Ampere force resulting from the interaction of the conducting tether with the Earth’s magnetic field. The mathematical model of motion is constructed using the Lagrange method taking into account the effect of the distributed loads from the Ampere force and the aerodynamic forces on the tether. It is shown that the motion of the system relative to the center of mass is unstable if the current is constant. It is proposed to use a linear regulator to stabilize the motion of the system with respect to the local vertical. Bellman’s dynamic programming principle is used to synthesize the regulator.
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REFERENCES
V. V. Beletskii and E. M. Levin, Dynamics of Space Cable Systems (Nauka, Moscow, 1990) [in Russian].
E. M. Levin, Dynamic Analysis of Space Tether Missions (Am. Astronaut. Soc., San Diego, 2007).
R. Zhong and Z. H. Zhu, “Dynamics of nanosatellite deorbit by bare electrodynamic tether in low earth orbit,” J. Spacecr. Rockets 50, 691–700 (2013).
E. M. Levin, “Stability of stationary equilibrium positions of electrodynamic cable systems in orbit,” Kosm. Issled. 25, 491–501 (1987).
J. Pelaez, T. C. Lorenzini, O. Lopez-Rebollal, and M. Ruiz, “A new kind of dynamic instability in electrodynamic tethers,” J. Astronaut. Sci. 48, 449–476 (2000).
R. Mantellato, M. Pertile, G. Colombatti, and E. C. Lorenzini, “Analysis of passive system to damp the libration of electrodynamic tethers for deorbiting,” in Proceedings of the AIAA SPACE 2013 Conference and Exposition (AIAA, San Diego, 2013), pp. 1–9.
M. Iñarrea, V. Lanchares, A. I. Pascual, and J. P. Salas, “Attitude stabilization of electrodynamic tethers in elliptic orbits by time-delay feedback control,” Acta Astronaut. 96, 280–295 (2014).
X. Zhou, J. Li, H. Baoyin, and V. Zakirov, “Equilibrium control of electrodynamic tethered satellite systems in inclined orbits,” J. Guidance, Control, Dyn. 29, 1451–1454 (2006).
J. Corsi and L. Iess, “Stability and control of electrodynamic tethers for de-orbiting applications,” Acta Astronaut. 48, 491–501 (2001).
P. S. Voevodin and Yu. M. Zabolotnov, “Modeling and analysis of oscillations of electrodynamic tether system on orbit of Earth satellite,” Mat. Model. 29 (6), 21–34 (2017).
F. Dignat and V. Shilen, “Control of oscillations of the orbital tether system,” Prikl. Mat. Mekh. 64. 747–754 (2000).
Yu. M. Zabolotnov and D. I. Fefelov, “Dynamics of movement of a capsule with a cable in the extra-atmospheric portion of descent from orbit,” Izv. SNTs RAN 8, 841–848 (2006).
R. Zhong and Z. H. Zhu, “Dynamic analysis of deployment and retrieval of tethered satellites using a hybrid hinged-rod tether model,” Int. J. Aerospace Lightweight Struct. 5, 1–21 (2015).
Yu. M. Zabolotnov, “Control of the deployment of an orbital tether system that consists of two small spacecraft,” Cosmic Res. 55, 224 (2017).
R. E. Bellman, Dynamic Programming (Princeton Univ. Press, Princeton, 2010).
A. M. Letov, Flight Dynamics and Control (Nauka, Moscow, 1969) [in Russian].
D. E. Okhotsimskiy and Yu. G. Sikharulidze, Basics of Space Flight Mechanics (Nauka, Moscow, 1990) [in Russian].
A. A. Dmitrievsky, N. M. Ivanov, L. N. Lysenko, and S. S. Bogodistov, Ballistics and Rocket Navigation (Mashinostroenie, Moscow, 1985) [in Russian].
N. S. Arzhannikov and G. S. Sadekova, Aerodynamics of Aircraft (Vyssh. Shkola, Moscow, 1983) [in Russian].
ACKNOWLEDGMENTS
This work was supported by the Russian Foundation for Basic Research, project no. 16-41-630637.
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Translated by O. Pismenov
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Voevodin, P.S., Zabolotnov, Y.M. Stabilizing the Motion of a Low-Orbit Electrodynamic Tether System. J. Comput. Syst. Sci. Int. 58, 270–285 (2019). https://doi.org/10.1134/S1064230719020175
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DOI: https://doi.org/10.1134/S1064230719020175