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Published February 2002 | public
Journal Article

Lyapunov-based transfer between elliptic Keplerian orbits

Abstract

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.

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.

Additional details

Created:
August 19, 2023
Modified:
October 20, 2023