The Poincaré model of rotation for the synchronous satellites

This communication aims at exploring the possible behaviors of the rotational dynamics of a body locked in 1:1 spin-orbit resonance, consisting of a rigid mantle and a triaxial fluid core, in the approximation of the Poincare model. For that we perform an extensive numerical study of the system in considering different possible parameters for the size and shape of the core. We find a classical equilibrium, that can be considered as an extension of the Cassini State 1, around which the influence of the size and polar flattening of the core are highlighted. Moreover, we find a condition for the instability of this equilibrium, that can result in a shift of several degrees of the orientation of the figure axis with respect to the angular momentum.