Non-linear equations for the rotation of a viscoelastic planet taking into account the influence of a liquid core

Non-linear equations governing the temporal evolution of the vector of instantaneous rotation are developed for an Earth with a homogeneous mantle having a viscoelastic Maxwell rheology and with a homogeneous inviscid fluid core.This general theory is investigated using the angular momentum theorem applied to the coupled core-mantle system. It allows to study the influence upon the planetary rotation of a quasi-rigid rotational motion in the liquid core. It also enables to investigate the consequences of excitation sources (e.g. pressure), located at the core-mantle interface. Especially, the influence of viscoelastic variations in the inertia tensors resulting from the rotation itself or from various excitation sources are detailed with the help of a Love number formalism. The equations of the linear theory for an elastic Earth with a liquid core, and the non-linear theory for a viscous planet with a quasi-fluid behavior are shown to be particular cases of our generalized system of equations. Some planetological applications may be derived from the quasi-fluid approximation.