Chaotic attitude motion of satellites under small perturbation torques

Abstract

In this paper, the chaotic attitude motion of dissipative satellites under small perturbation torques is investigated by using the Deprit's canonical variables in the standard Hamiltonian form. Melnikov's integral is used to predict the transversal intersections of the stable and unstable manifolds for the satellites in perturbation. The theoretical criterion of chaotic attitude motion of the perturbed satellites will be derived from the Melnikov integral. Two models of satellites are studied. The first model is a quasi-rigid, energy- dissipating satellite subject to the time-periodic, non-Hamiltonian perturbation torques. The second model is a gyrostat satellite under small perturbation torques. It will be shown that, in terms of Deprit's variables, the equations of the attitude motion of the satellites can be easily transformed into the Hamiltonian form which is suitable for the application of Melnikov's method to some cases of complex, small perturbation torques.