Chaotic rotations of a liquid-filled solid

Abstract

The disturbed Hamiltonian equations of a solid filled with a rotating ellipsoidal mass of a liquid and subjected to small-applied moments are revisited using Deprit's variables. We investigate the chaotic dynamics of the orbiting liquid-filled solid and of the liquid-filled solid sliding and rolling on a perfectly smooth plane, in either energy-conservative or energy-dissipative conditions, when appropriately perturbed. Criteria for the judgment of potential chaotic rotations of the perturbed system are formulated by means of Melnikov–Holmes–Marsden (MHM) integrals. Strategies for the solution of heteroclinic orbits of the symmetrical liquid-filled solid under torque-free conditions are outlined theoretically. Physical parameters that will probably trigger the onset of chaotic motions can be determined accordingly. Results from MHM algorithms are crosschecked with Poincare sections together with Lyapunov characteristic exponents.