Chaotic attitude maneuvers in spacecraft with a completely liquid-filled cavity

This paper investigates the problem of chaotic dynamics in attitude transition maneuvers. We consider the case of a rigid body with a completely liquid-filled cavity, whose spin changes from the minor axis to the major axis under the influence of viscous damping and low-amplitude oscillating perturbations expressed as external torques. The Melnikov integral is used to predict transversal intersections of the perturbed system's stable and unstable manifolds. After discussing the phase space of the system, the equations of motion are transformed into a form more suitable for the application of Melnikov's method. Melnikov's method yields an analytical criterion for homoclinic chaos, in the form of an inequality written in terms of the system parameters. In addition, the prediction of the Melnikov criterion is compared to numerical simulations of the system. Finally, we investigate the dependence of chaotic dynamics on quantities such as body shape, degree of damping, and frequency of the perturbing torques.