Chaos in nonlinear planar oscillation of a satellite in an elliptical orbit under the influence of third body torque (Q1355410)

We study the planar oscillation of a satellite in an elliptic orbit under the influence of third body torque. By using Melnikov's method, we prove that the equations of motion are non-integrable. The Bogolyubov-Krylov-Mitropol'ski method (BKM) is employed to establish that the amplitude of the oscillation remains constant up to the second order of approximation. The main and parametric resonances are shown to exist and are studied by BKM method. The theory is applied to the rotational motion of Hyperion, a satellite of Saturn. It is observed that Hyperion tumbles chaotically, and, as the third-body torque parameter increases, it tumbles more chaotically.