February  2002, 2(1): 57-67. doi: 10.3934/dcdsb.2002.2.57

Lyapunov-based transfer between elliptic Keplerian orbits

1. 

Control and Dynamical Systems 107-81, California Institute of Technology, Pasadena, CA 91125, United States, United States, United States

Received  August 2001 Revised  September 2001 Published  November 2001

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.
Citation: Dong Eui Chang, David F. Chichka, Jerrold E. Marsden. Lyapunov-based transfer between elliptic Keplerian orbits. Discrete & Continuous Dynamical Systems - B, 2002, 2 (1) : 57-67. doi: 10.3934/dcdsb.2002.2.57
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