Chaotic Attitude Motion of a Satellite on a Keplerian Elliptic Orbit

Abstract

In this paper, we discussed an asymmetric satellite moving on a Keplerian elliptic orbit in a gravitationalfield of a central mass point. Formulating the Hamiltonian of the rigid body in Serret-Andoyer variables, and by an infinitesimal contact transformation, the system is reduced to a rigid body in torque-free motion, but its moments of inertia vary with time, we take this system as an Euler-Poinsot motion perturbed by a small periodic excitation, then we can apply the Melnikov method to determine the intersection of the stable and unstable manifold of the system’s hyperbolic point, usually this can be the cause of chaos. We also manifested the chaotic motion in angular momentum space by the Poincare surface of section.