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Celestial Mechanics and Dynamical Astronomy

, Volume 125, Issue 3, pp 309–332 | Cite as

Three-dimensional multi-tethered satellite formation with the elements moving along Lissajous curves

  • D. Yarotsky
  • V. Sidorenko
  • D. PritykinEmail author
Original Article

Abstract

This note presents a novel approach to maintain three-dimensional multi-tethered satellite formation in space. For a formation consisting of a main body connected by tethers with several deputy satellites (the so-called “hub-and-spoke” configuration) we demonstrate that under proper choice of the system’s parameters the deputy satellites can move along Lissajous curves in the plane normal to the local vertical with all tethers stretched; the total force due to the tension forces acting on the main satellite is balanced in a way allowing it to be in relative equilibrium strictly below or strictly above the system’s center of mass. We analyze relations between the system’s essential parameters and obtain conditions under which the proposed motion does take place. We also study analytically the motion stability for different configurations and whether the deputy satellites can collide or the tethers can entangle. Our theoretical findings are corroborated and validated by numerical experiments.

Keywords

Tethered satellite system Hub-and-spoke configuration Perturbation theory Collision  Tethers entanglement Stability 

Notes

Acknowledgments

The authors first conceived the idea of the motion described in this paper during the dynamical analysis of the rotating multi-tethered satellite system (Alary et al. 2015), and the authors sincerely thank their collaborators Didier Alary, Kirill Andreev, Pavel Boyko, Elena Ivanova, and Cyrille Tourneur for the warm and stimulating atmosphere of that study. The work of one of the authors (DY) on the present paper was supported by Russian Science Foundation (Project 14-50-00150).

Supplementary material

Supplementary material 1 (avi 24262 KB)

References

  1. Alary, D., Andreev, K., Boyko, P., Ivanova, E., Pritykin, D., Sidorenko, V., et al.: Dynamics of multi-tethered pyramydal satellite formation. Acta Astronaut. 117, 222–232 (2015)ADSCrossRefGoogle Scholar
  2. Armstrong, M.A.: Basic Topology. Springer, New York (1983)CrossRefzbMATHGoogle Scholar
  3. Arnold, V.I.: Ordinary Differential Equations. MIT Press, Cambridge (1978)Google Scholar
  4. Avanzini, G., Fedi, M.: Refined dynamical analysis of multi-tethered satellite formations. Acta Astronaut. 84, 36–48 (2013)ADSCrossRefGoogle Scholar
  5. Avanzini, G., Fedi, M.: Effects of eccentricity of the reference orbit on multi-tethered satellite formations. Acta Astronaut. 94, 338–350 (2014)ADSCrossRefGoogle Scholar
  6. Bekey, I.: Tethers open new space options. Astronaut. Aeronaut. 21, 23–40 (1983)ADSCrossRefGoogle Scholar
  7. Cai, Z., Zhao, J., Peng, H., Qi, Z.: Nonlinear control of rotating multi-tethered formations in Halo orbits. Int. J. Comput. Methods 11, 1344008 (2014). (26 pages)MathSciNetCrossRefGoogle Scholar
  8. Celletti, A., Sidorenko, V.V.: Some properties of dumbbell satellite attitude dynamics. Celest. Mech. Dyn. Astron. 101, 105–126 (2008)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  9. Clohessy, W.H., Wiltshire, R.S.: Terminal guidance system for satellite rendezvous. J. Aerosp. Sci. 27, 653–658 (1960)CrossRefzbMATHGoogle Scholar
  10. Gantmacher, F.R.: Applications of the Theory of Matrices. Interscience, New York (1959)zbMATHGoogle Scholar
  11. Nayfeh, A.H.: Perturbations Methods. Wiley-Interscience, New York (1973)Google Scholar
  12. Panosian, S., Seubert, C.R., Schaub, H.: Tethered Coulomb structure applied to close proximity situational awareness. AIAA J. Spacecr. Rockets 49, 1183–1193 (2012)ADSCrossRefGoogle Scholar
  13. Pizarro-Chong, A., Misra, A.K.: Dynamics of multi-tethered satellite formations containing a parent body. Acta Astronaut. 63, 1188–1202 (2008)ADSCrossRefGoogle Scholar
  14. Seubert, C.R., Schaub, H.: Tethered Coulomb structures: prospects and challenges. J. Astronaut. Sci. 57, 347–348 (2009)ADSCrossRefGoogle Scholar
  15. Seubert, C.R., Panosian, S., Schaub, H.: Attitude and power analysis of multi-tethered two-node tethered Coulomb structures. AIAA J. Spacecr. Rockets 48, 1033–1045 (2011)ADSCrossRefGoogle Scholar
  16. Sidorenko, V.V., Celletti, A.: A “spring-mass” model of tethered satellite systems: properties of planar periodic motions. Celest. Mech. Dyn. Astron. 107, 209–231 (2010)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  17. Wong, B., Misra, A.: Planar dynamics of variable length multi-tethered spacecraft near collinear Lagrangian points. Acta Astronaut. 63, 1178–1187 (2008)ADSCrossRefGoogle Scholar
  18. Zhao, J., Cai, Z.: Nonlinear dynamics and simulation of multi-tethered satellite formations in Halo orbits. Acta Astronaut. 63, 673–681 (2008)ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2016

Authors and Affiliations

  1. 1.Institute for Information Transmission ProblemsRussian Academy of SciencesMoscowRussia
  2. 2.Keldysh Institute of Applied MathematicsRussian Academy of SciencesMoscowRussia
  3. 3.Moscow Institute of Physics and TechnologyDolgoprudny, Moscow RegionRussia

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