Lyapunov-based transfer between elliptic Keplerian orbits

Pages: 57 - 67, Volume 2, Issue 1, February 2002

doi:10.3934/dcdsb.2002.2.57       Abstract        Full Text (212.7K)       Related Articles

Dong Eui Chang - Control and Dynamical Systems 107-81, California Institute of Technology, Pasadena, CA 91125, United States (email)
David F. Chichka - Control and Dynamical Systems 107-81, California Institute of Technology, Pasadena, CA 91125, United States (email)
Jerrold E. Marsden - Control and Dynamical Systems 107-81, California Institute of Technology, Pasadena, CA 91125, United States (email)

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.

Keywords:  Satellite dynamics, feedback stabilization, orbit transfer.
Mathematics Subject Classification:  70F05, 93D15, 93D20.

Received: August 2001;      Revised: September 2001;      Published: November 2001.