Secular evolution of a rigid body with fluid-filled cavity in the two-body problem

Lucas Ruiz dos Santos -  Universidade Federal de Itajubá

Abstract:

We modify a three-dimensional Hamiltonian model of a celestial body composed of a rigid mantle and a fluid-filled cavity

by incorporating core-mantle viscous friction and tidal forces. We study the secular rotational evolution of the system and apply singular perturbation theory to derive the averaged dynamics of the mantle's spin under this viscous coupling.

We analyze the stability of the equilibria in the secular system across the full  range of parameters.

We also apply the theory to the analysis of the Moon's libration.