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On Stability of the Motion of Electrodynamic Tether System in Orbit Near the Earth

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Abstract

Algorithms for stabilizing the motion of an electrodynamic tether system in the orbit of an Earth satellite are analyzed. The system under consideration consists of two small spacecraft and a tether connecting them. A tether system is designed to change its orbital parameters, using the interaction of a current-conducting tether with the Earth’s magnetic field. Several mathematical models are used to describe the movement of the system, with varying degrees of detail describing its movement. An algorithm for stabilizing the movement of the tether system in the vicinity of the local vertical is proposed. A feature of the considered algorithm, based on the feedback principle, is the stabilization of the bending vibrations of the tether from the action of the distributed load acting on the current-conducting tether in a magnetic field. It is shown that not taking into account the bending vibrations of the tether in the stabilization algorithms can lead not only to a deterioration in the quality of stabilization, but also to a loss of stability of the system motion (its transition to rotation).

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References

  1. V. V. Beletskii and E. M. Levin, Dynamics of Space Tether Systems (Nauka, Moscow, 1965) [in Russian].

    Google Scholar 

  2. E. M. Levin, Dynamic Analysis of Space Tether Missions (American Astronautical Society, San Diego, 2007).

    Google Scholar 

  3. R. Zhong and Z. H. Zhu, “Dynamics of Nanosatellite Deorbit by Bare Electrodynamic Tether in Low Earth Orbit,” J. Spac. Rock. 50 (3), 691–700 (2013).

    Article  Google Scholar 

  4. X. Chen and J. R. Sanmartin, “Bare-Tether Cathodic Contact through Thermionic Emission by Low-Workfunction Materials,” Phys. Plasm. 19, 1–8 (2012).

    Google Scholar 

  5. R. Zhong and Z. H. Zhu, “Optimal Control of Nanosatellite Fast Deorbit Using Electrodynamic Tether,” J. Guid. Cont. Dyn. 37 (4), 1182–1194 (2014).

    Article  ADS  Google Scholar 

  6. K. R. Fuhrhop, Theory and Experimental Evaluation of Electrodynamic Tether Systems and Related Technologies, PhD Dissertation (University of Michigan, 2007).

  7. E. M. Levin, “Stability of Steady-State Motions of an Electromagnetic Rope System in Orbit,” Kosm. Issl. 25(4), 491–501 (1987).

    Google Scholar 

  8. J. Pelaez, T. C. Lorenzini, O. Lopez-Rebollal, and M. Ruiz, “A new Kind of Dynamic Instability in Electrodynamic Tethers,” J. Astr. Sci. 48(4), 449–476 (2000).

    Google Scholar 

  9. H. Kojima and T. Sugimoto, “Stability Analysis of In-Plane and Out-of-Plane Periodic Motions of Electrodynamic Tether System in Inclined Elliptic Orbit,” Acta Astr. 65, 477–488 (2009).

    Article  ADS  Google Scholar 

  10. R. Mantellato, M. Pertile, G. Colombatti, and E. C. Lorenzini, “Analysis of Passive System to Damp the Libration of Electrodynamic Tethers for Deorbiting,” in AIAA SPACE 2013 Conference and Exposition, San Diego, AIAA 2013–5390 (AIAA, San Diego, 2013), pp. 1–9.

    Google Scholar 

  11. 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 Astr. 96, 280–295 (2014).

    Article  ADS  Google Scholar 

  12. X. Zhou, J. Li, H. Baoyin, and V. Zakirov, “Equilibrium Control of Electrodynamic Tethered Satellite Systems in Inclined Orbits,” J. Guid. Cont. Dyn. 29 (6), 1451–1454 (2006).

    Article  ADS  Google Scholar 

  13. J. Corsi and L. Iess, “Stability and Control of Electrodynamic Tethers for De-Orbiting Applications,” Acta Astr. 48 (5–12), 491–501 (2001).

    Article  ADS  Google Scholar 

  14. Yu. M. Zabolotnov and D. I. Fefelov, “Dynamics of the Tethered Capsule Motion in the Extra-Atmospheric Disorbit Segment,” Izv. Samar. Nauchn. Tsentra Ros. Akad. Nauk 8(3), 841–848 (2006).

    Google Scholar 

  15. F. Dignath and W. Schiehlen, “Control of the Vibrations of a Tethered Satellite System,” Prikl. Mat. Mekh. 64(5), 747–754 (2000)

    MATH  Google Scholar 

  16. F. Dignath and W. Schiehlen, [J. Appl. Math. Mech. (Engl. Transl.) 64(5), 715–722 (2000)].

    Article  Google Scholar 

  17. 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).

    MathSciNet  MATH  Google Scholar 

  18. R. Zhong and Z. H. Zhu, “Dynamic Analysis of Deployment and Retrieval of Tethered Satellites Using a Hybrid Hinged-Rod Tether Model,” Int. J. Aer. Ligh. Struct. (IJALS) 5 (1), 1–21 (2015).

    MathSciNet  Google Scholar 

  19. Yu. M. Zabolotnov “Control of the Deployment of an Orbital Tether System that Consists of Two Small Spacecraft,” Kosm. Issl. 55(3), 236–246 (2017)

    Google Scholar 

  20. Yu. M. Zabolotnov [Cosmic Res. (Engl. Transl.) 55, 224–233 (2017)].

    Article  Google Scholar 

  21. N. N. Bogolyubov and Yu. A. Mitropol’skii, Asymptotic Methods in Theory of Nonlinear Oscillations (Nauka, Moscow, 1974) [in Russian].

    MATH  Google Scholar 

  22. R. Bellman, Dynamic Programming (Princeton Univ. Press, Princeton, 1957; Izd. Inostr. Lit., Moscow, 1960).

    MATH  Google Scholar 

  23. F. L. Chernousko, L. D. Akulenko, and B. N. Sokolov, Control of Oscillations (Nauka, Moscow, 1980) [in Russian].

    Google Scholar 

  24. N. N. Moiseev, Asymptotic Methods of Nonlinear Mechanics (Nauka, Moscow, 1986) [in Russian].

    Google Scholar 

  25. V. V. Salmin, S. A. Ishkov, and O. L. Starinova, Methods for Solving Variational Problems of Mechanics of Space Flight with Small Traction (Izdat. SNTs RAN, Samara, 2006) [in Russian].

    Google Scholar 

  26. L. D. Akulenko, Asymptotic Methods of Optimal Control (Nauka, Moscow, 1987) [in Russian].

    MATH  Google Scholar 

  27. Yu. M. Zabolotnov and A. A. Lobanov, “Synthesis of a Controller for Stabilizing the Motion of a Rigid Body about a Fixed Point,” Izv. Ros. Akad. Nauk. Mekh. Tv. Tela, No. 3, 59–71 (2007)

  28. Yu. M. Zabolotnov and A. A. Lobanov, [Mech. Sol. (Engl. Transl.) 52 (3), 278–288 (2017)].

    Google Scholar 

  29. M. M. Khapaev, Averaging in Stability Theory (Nauka, Moscow, 1988) [in Russian].

    Google Scholar 

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Acknowledgement

This work was supported by a grant from the RFBR RF 16-41-630637.

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Authors and Affiliations

  1. S. P. Korolev Samara National Research University, Moskovskoe sh. 34, Samara, 443086, Russia

    P. S. Voevodin & Yu. M. Zabolotnov

Authors
  1. P. S. Voevodin
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  2. Yu. M. Zabolotnov
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Correspondence to Yu. M. Zabolotnov.

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Russian Text © The Author(s), 2019, published in Izvestiya Akademii Nauk, Mekhanika Tverdogo Tela, 2019, No. 4, pp. 48–62.

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Voevodin, P.S., Zabolotnov, Y.M. On Stability of the Motion of Electrodynamic Tether System in Orbit Near the Earth. Mech. Solids 54, 890–902 (2019). https://doi.org/10.3103/S0025654419060050

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  • DOI: https://doi.org/10.3103/S0025654419060050

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