Lyapunov-based Transfer between Elliptic Keplerian Orbits

Chang, D., D. Chichka and J. E. Marsden

Discrete and Continuous Dynamical Systems - Series B 2, 57-67

Abstract:

We present a study of transfer 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 an 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.