A Study of the Motion of Four Linked Satellites Controlled Using Lorentz Forces

K. S. Chernov; Чернов К. С.; D. S. Ivanov; Иванов Д. С.

doi:10.31857/S0023420623600022

A Study of the Motion of Four Linked Satellites Controlled Using Lorentz Forces

Autores: Chernov K.S.¹, Ivanov D.S.¹
Afiliações:
1. Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow, Russia
Edição: Volume 61, Nº 4 (2023)
Páginas: 339-352
Seção: Articles
URL: https://rjmseer.com/0023-4206/article/view/672640
DOI: https://doi.org/10.31857/S0023420623600022
EDN: https://elibrary.ru/UMATAE
ID: 672640

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Resumo

This paper considers four satellites connected to each other by electrodynamic tethers, which are assumed to be rigid in the mathematical model of the system’s motion. In the Earth’s magnetic field, current-carrying conductors are affected by Lorentz forces, which are used to control the motion of the system’s center of mass and the angular motion. The paper presents an algorithm for calculating the magnitude of the current to stop the drift of the center of mass of a tetrahedral formation relative to the desired orbital reference frame in low Earth orbit and spin the system up to a constant angular velocity relative to the center of mass. A numerical study of the convergence time to achieve the required motion is carried out depending on the maximum possible current and initial conditions.

Sobre autores

K. Chernov

Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow, Russia

Email: chernow.kirill@gmail.com
Россия, Москва

D. Ivanov

Keldysh Institute of Applied Mathematics, Russian Academy of Sciences, Moscow, Russia

Autor responsável pela correspondência
Email: chernow.kirill@gmail.com
Россия, Москва

Bibliografia

Shirobokov M.G., Trofimov S.P. Adaptive Neural Formation-Keeping Control for Satellites in a Low-Earth Orbit // Cosmic Research. 2021. V. 59. Iss. 6. P. 501–516. https://doi.org/10.1134/S0010952521060113
Leonard C.L. Formationkeeping of Spacecraft via Differential Drag. Master Thesis. Massachusetts Inst. Technol., 1986. http://hdl.handle.net/1721.1/13358
Mashtakov Y., Ovchinnikov M., Petrova T. et al. Two-satellite formation flying control by cell-structured solar sail // Acta Astronaut. 2020. V. 170. P. 592–600. https://doi.org/10.1016/j.actaastro.2020.02.024
Ivanov D., Gondar R., Monakhova U. et al. Electromagnetic uncoordinated control of a ChipSats swarm using magnetorquers // Acta Astronaut. 2022. V. 192. P. 15–29. https://doi.org/10.1016/j.actaastro.2021.12.014
Shestakov S., Ivanov D., Ovchinnikov M. Formation-Flying Momentum Exchange Control by Separate Mass // J. Guid. Control. Dyn. 2015. V. 38. Iss. 8. P. 1–10. https://doi.org/10.2514/1.G001137
Peck M.A., Streetman B., Saaj C.M., Lappas V. Spacecrat Formation Flying Using Lorentz Forces // J. Br. Interplanet. Soc. 2007. V. 60. Iss. 7. P. 263–267.
Peck M.A. Prospects and challenges for Lorentz-augmented orbits // Collect. Tech. Papers – AIAA Guid. Navig. Control Conf. 2005. V. 3. P. 1631–1646. https://doi.org/10.2514/6.2005-5995
Schaffer L., Burns J.A. Charged dust in planetary magnetospheres: Hamiltonian dynamics and numerical simulations for highly charged grains // J. Geophys. Res. SP. Phys. 1994. V. 99. Iss. A9. P. 17211–17223.https://doi.org/10.1029/94JA01231
Saaj C.M., Lappas V., Richie D. et al. Electrostatic forces for satellite swarm navigation and reconfiguration. Final report for Ariadna Study Id. AO 4919 05. ESA, 2006. 96 p.
Liu J., Gangqiang L., Zhu Z.H. et al. Automatic orbital maneuver for mega-constellations maintenance with electrodynamic tethers // Aerospace Science and Technology. 2020. V. 105. Art. ID. 105910. https://doi.org/10.1016/j.ast.2020.105910
Yang Y.-W., Cai H. Extended time–delay autosynchronization method for libration control of electrodynamic tether using Lorentz force // Acta Astronaut. 2019. V. 159. P. 179–188. https://doi.org/10.1016/j.actaastro.2019.03.038
Lu H., Li A., Wang C., Zabolotnov Y. Stability analysis and motion control of spinning electrodynamic tether system during transition into spin // Acta Astronaut. 2020. V. 177. 2019. P. 871–881. https://doi.org/10.1016/j.actaastro.2019.11.032
Voevodin P.S., Zabolotnov Y.M. Analysis of the Dynamics and Choice of Parameters of an Electrodynamic Space Tether System in the Thrust Generation Mode // Cosm. Res. 2020. V. 58. Iss. 1. P. 42–52. https://doi.org/10.1134/S0010952520010062
Ohkawa Y., Kawamoto S., Okumura T. et al. Review of KITE – Electrodynamic tether experiment on the H-II Transfer Vehicle // Acta Astronaut. 2020. V. 177. 2019. P. 750–758. https://doi.org/10.1016/j.actaastro.2020.03.014
Kalenova V.I., Morozov V.M. Stabilization of Satellite Relative Equilibrium Using Magnetic and Lorentzian Moments // Cosm. Res. 2021. V. 59. Iss. 5. P. 343–356. https://doi.org/10.1134/S0010952521050051
Alexandrov A.Y., Tikhonov A.A. Electrodynamic Control with Distributed Delay for AES Stabilization in an Equatorial Orbit // Cosm. Res. 2022. V. 60. Iss. 5. P. 366–374. https://doi.org/10.1134/S0010952522040013
Kalenova V.I., Morozov V.M. Novel approach to attitude stabilization of satellite using geomagnetic Lorentz forces // Aerospace Science and Technology. 2020. V. 106. Iss. 1. Art. ID. 106105. https://doi.org/10.1016/j.ast.2020.106105
Guzmán J.J., Edery A. Mission design for the MMS tetrahedron formation // IEEE Aerosp. Conf. Proc. 2004. V. 1. P. 533–540. https://doi.org/10.1109/AERO.2004.1367637
Shestakov S., Ovchinnikov M., Mashtakov Y. Analytical approach to construction of tetrahedral satellite formation // J. Guid. Control. Dyn. 2019. V. 42. Iss. 12. P. 2600–2614. https://doi.org/10.2514/1.G003913
Guerman A.D., Smirnov G.V., Paglione P., Seabra A.M.V. Stationary configurations of a tetrahedral tethered satellite formation // J. Guid. Control. Dyn. 2008. V. 31. Iss. 2. P. 424–428. https://doi.org/10.2514/1.31979
Hill G.W. Researches in the Lunar Theory // Am. J. Math. 1878. V. 1. P. 5–26.
Ivanov D., Monakhova U., Ovchinnikov M. Nanosatellites swarm deployment using decentralized differential drag-based control with communicational constraints // Acta Astronaut. 2019. V. 159. P. 646–657. https://doi.org/10.1016/j.actaastro.2019.02.006
Mashtakov Y.V., Ovchinnikov M.Y., Tkachev S.S. Study of the disturbances effect on small satellite route tracking accuracy // Acta Astronaut. 2016. V. 129. P. 22–31. https://doi.org/10.1016/j.actaastro.2016.08.028
Барбашин Е.А. Введение в теорию устойчивости. М.: Наука, 1967.
Кюнци Г.П., Крелле В. Нелинейное программирование. М.: Советское радио, 1965.