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Lyapunov-based transfer between elliptic Keplerian orbits

Chang, Dong Eui and Chichka, David F. and Marsden, Jerrold E. (2002) Lyapunov-based transfer between elliptic Keplerian orbits. Discreet and Continuous Dynamical Systems Series B, 2 (1). pp. 57-67. ISSN 1531-3492. doi:10.3934/dcdsb.2002.2.57.

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We present a study of the transfer of satellites between elliptic Keplerian orbits using Lyapunov stability theory specific to this problem. The construction of Lyapunov functions is based on the fact that a non-degenerate Keplerian orbit is uniquely described by its angular momentum and Laplace (- Runge-Lenz) vectors. We suggest a Lyapunov function, which gives a feedback controller such that the target elliptic orbit becomes a locally asymptotically stable periodic orbit in the closed-loop dynamics. We show how to perform a global transfer between two arbitrary elliptic orbits based on the local transfer result. Finally, a second Lyapunov function is presented that works only for circular target orbits.

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Additional Information:© AIMS 2001. Received:August 2001. Revised:September 2001 Published:November 2001. D. E. Chang is partially supported by the California Institute of Technology and AFOSR grant F49620-99-1-0190. D. F. Chichka is partially supported by AFOSR grant F49620-99-1-0190. J. E. Marsden is partially supported by the California Institute of Technology and NSF-KDI grant ATM-9873133.
Funding AgencyGrant Number
California Institute of TechnologyUNSPECIFIED
Air Force Office of Scientific Research (AFOSR)F49620-99-1-0190
NSF-Knowledge and Distributed Intelligence (KDI)ATM-9873133
Subject Keywords:Satellite dynamics, feedback stabilization, orbit transfer.
Issue or Number:1
Classification Code:MSC: 70F05, 93D15, 93D20
Record Number:CaltechAUTHORS:20100728-074530525
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:19204
Deposited By: Ruth Sustaita
Deposited On:29 Jul 2010 23:10
Last Modified:08 Nov 2021 23:50

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