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Lorentz Force Formation Flying in the Earth-Moon System

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Low Energy Flight: Orbital Dynamics and Mission Trajectory Design
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Abstract

We analyse a dynamical scenario where a constantly charged spacecraft (follower) moves in the vicinity of another one (leader) that follows a circular Keplerian orbit around the Earth and generates a rotating magnetic dipole. The mass of the follower is assumed to be negligible when compared with the one of the leader and both spacecrafts are supposed to be in a high-Earth orbit, so the Lorentz force on the follower due to the geomagnetic field is ignored. With these assumptions, the motion of the leader is not perturbed by the follower and is only subjected to the Earth’s gravitational force, while the charged follower is subject to both the gravitational force of the Earth and the Lorentz force due to the magnetic dipole of the leader.

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References

  1. E. Anderson, Z. Bai et al., LAPACK Users’ Guide, 3rd edn., Society for Industrial and Applied Mathematics (1999)

    Google Scholar 

  2. J. Atchison, M. Peck, Lorentz-augmented Jovian orbit insertion. J. Guid. Control Dyn. 32(2), 418–425 (2009)

    Article  Google Scholar 

  3. N. Baresi, Z.P. Olikara, D.J. Scheeres, Survey of numerical methods for computing quasi-periodic tori in Astrodynamics, in 26th AAS/AIAA Space Flight Mechanics Meeting, Napa, CA (2016)

    Google Scholar 

  4. B. Baudouy, Heat transfer and cooling techniques at low temperature (2015), arXiv:1501.07153

  5. L.S. Breger, P. Gurfil, K.T. Alfriend, S.R. Vadali, J.P. How, Spacecraft Formation Flying (Elsevier Ltd, New York, 2010)

    Google Scholar 

  6. G. Gómez, J.M. Mondelo, The dynamics around the collinear equilibrium points of the RTBP. Phys. D: Nonlinear Phenom. 157(4), 283–321 (2001)

    Article  MathSciNet  Google Scholar 

  7. G. Gómez, J. Llibre, R. Martínez, C. Simó, Dynamics and Mission Design Near Libration Points, Vol. I Fundamentals: The Case of Collinear Libration Points (World Scientific, Singapore, 2001)

    Google Scholar 

  8. G. Gómez, M. Marcote, High-order analytical solutions of Hill’s equations. Celest. Mech. Dyn. Astron. 94(2), 197–211 (2006)

    Article  MathSciNet  Google Scholar 

  9. À. Haro, M. Canadell, J.L. Figueras, A. Luque, J.M. Mondelo, The Parameterization Method for Invariant Manifolds (Springer, Berlin, 2016)

    Book  Google Scholar 

  10. M.E. Hough, Lorentz force perturbations of a charged ballistic missile, in Proceedings of the AIAA Guidance and Control Conference, AIAA-1982-1549, San Diego, CA (1982)

    Google Scholar 

  11. R.S. Irving, Integers, Polynomials, and Rings (Springer, Berlin, 2004)

    MATH  Google Scholar 

  12. À. Jorba, J. Villanueva, On the persistence of lower Cdimensional invariant tori under quasiCperiodic perturbations. J. Nonlinear Sci. 7, 427–473 (1997)

    Article  MathSciNet  Google Scholar 

  13. L.B. King, G.G. Parker, S. Deshmukh, J.H. Chong, Study of interspacecraft Coulomb forces and implications for formation flying. J. Propuls. Power 19(3), 497–505 (2003)

    Article  Google Scholar 

  14. E. Kolemen, N.J. Kasdin, P. Gurfil, Multiple Poincaré sections method for finding the quasiperiodic orbits of the restricted three body problem. Celest. Mech. Dyn. Astron. 112(1), 47–74 (2012)

    Article  Google Scholar 

  15. E. Kong, D. Kwon, S. Schweighart, L. Elias, R. Sedwick, D. Miller, Electromagnetic formation flight for multi-satellite arrays. J. Spacecr. Rocket. 41(4), 659–666 (2004)

    Article  Google Scholar 

  16. D.W. Kwon, Propellantless formation flight applications using electromagnetic satellite formations. Acta Astronaut. 67(9–10), 1189–1201 (2010)

    Article  Google Scholar 

  17. D.W. Kwon, R.J. Sedwick, Cryogenic heat pipe for cooling high-temperature superconducting coils. J. Thermophys. Heat Transf. 23(4), 732–740 (2012)

    Article  Google Scholar 

  18. K. Meyer, G. Hall, D. Offin, Introduction to Hamiltonian Dynamical Systems and the N-Body Problem (Springer Science & Business Media, Berlin, 2008)

    MATH  Google Scholar 

  19. M.A. Peck, Prospects and challenges for Lorentz-augmented orbits, in Proceedings of the AIAA Guidance, Navigation, and Control Conference, AIAA-2005-5995, San Francisco, CA (2005)

    Google Scholar 

  20. M.A. Peck, B. Streetman, C.M. Saaj, V. Lappas, Spacecraft formation flying using Lorentz forces. J. Br. Interplanet. Soc. 60(7), 263–267 (2007)

    Google Scholar 

  21. C. Peng, Relative motion and satellite formation based on Lorentz force (in chinese) (Graduate University of Chinese Academy of Sciences, Master diss., 2012)

    Google Scholar 

  22. C. Peng, Relative orbital motion of a charged object near a spaceborne radially-directed rotating magnetic dipole, in66th International Astronautical Congress, Jerusalem (2015)

    Google Scholar 

  23. C. Peng, Y. Gao, Formation-flying planar periodic orbits in the presence of inter-satellite Lorentz force. IEEE Trans. Aerosp. Electron. Syst. (2017)

    Google Scholar 

  24. A.K. Porter, D.J. Alinger, R.J. Sedwick, J. Merk, R.A. Opperman, A. Buck, G. Eslinger, P. Fisher, D.W. Miller, E. Bou, Demonstration of electromagnetic formation flight and wireless power transfer. J. Spacecr. Rocket. 51(6), 1914–1923 (2014)

    Google Scholar 

  25. Y. Ren, J.J. Masdemont, M. Marcote, G. Gómez, Computation of analytical solutions of the relative motion about a Keplerian elliptic orbit. Acta Astronaut.81(1), 186–199 (2012)

    Google Scholar 

  26. C.M. Saaj, V. Lappas, D. Richie, M. Peck, B. Streetman, H. Schaub, Electrostatic forces for satellite swarm navigation and reconfiguration - Final report, Final Report for Ariadna Study Id. AO491905 (2006)

    Google Scholar 

  27. L. Schaffer, J.A. Burns, Charged dust in planetary magnetospheres: Hamiltonian dynamics and numerical simulations for highly charged grains. J. Geophys. Res. 9(A9), 17211–17223 (1994)

    Article  Google Scholar 

  28. C. Simó: On the analytical and numerical approximation of invariant manifolds. In D. Benest, C. Froeshlé, (eds.), Modern methods in Celestial Mechanics: 285C330. Editions Frontires (1990)

    Google Scholar 

  29. L.A. Sobiesiak, C.J. Damaren, Controllability of Lorentz-augmented spacecraft formations. J. Guid. Control. Dyn. 38(11), 2188–2195 (2015)

    Article  Google Scholar 

  30. J. Stoer, R. Bulirsch, Introduction to Numerical Analysis, vol. 12 (Springer Science & Business Media, Berlin, 2013)

    MATH  Google Scholar 

  31. B. Streetman, M.A. Peck, New synchronous orbits using the geomagnetic Lorentz force. J. Guid., Control. Dyn. 30(6), 1677–1690 (2007)

    Article  Google Scholar 

  32. B. Streetman, M.A. Peck, A general bang-bang control method for lorentz augmented orbits, in AAS Spaceflight Mechanics Meeting, AAS Paper 08-111, Galveston, Texas (2008)

    Google Scholar 

  33. B. Streetman, M.A. Peck, Gravity-assist maneuvers augmented by the Lorentz force. J. Guid. Control Dyn. 32(5), 1639–1647 (2009)

    Article  Google Scholar 

  34. S. Tsujii, M. Bando, H. Yamakawa, Spacecraft formation flying dynamics and control using the geomagnetic Lorentz force. J. Guid. Control Dyn. 36(1), 136–148 (2012)

    Article  Google Scholar 

  35. A. Umair, D.W. Miller, J.L. Ramirez, Control of electromagnetic satellite formations in near-Earth orbit. J. Guid. Control Dyn. 33(6), 1883–1891 (2010)

    Article  Google Scholar 

  36. D. Vokrouhlicky, The Geomagnetic effects on the motion of electrically charged artificial satellite. Celest. Mech. Dyn. Astron. 46(1), 85–104 (1989)

    Article  MathSciNet  Google Scholar 

  37. Y. Yu, H. Baoyin, Y. Jiang, Constructing the natural families of periodic orbits near irregular bodies. Mon. Not. R. Astron. Soc. 453(3), 3269–3277 (2015)

    Article  Google Scholar 

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Correspondence to Jianping Yuan .

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Yuan, J., Cheng, Y., Feng, J., Sun, C. (2019). Lorentz Force Formation Flying in the Earth-Moon System . In: Low Energy Flight: Orbital Dynamics and Mission Trajectory Design. Springer, Singapore. https://doi.org/10.1007/978-981-13-6130-2_4

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  • DOI: https://doi.org/10.1007/978-981-13-6130-2_4

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  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-13-6129-6

  • Online ISBN: 978-981-13-6130-2

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