  We revisit the rotation dynamics of a rigid satellite with either a liquid
core or a global sub-surface ocean. In both problems, the flow of the fluid
component is assumed inviscid. The study of a hollow satellite with a liquid
core is based on the Poincare-Hough model which provides exact equations of
motion. We introduce an approximation when the ellipticity of the cavity is
low. This simplification allows to model both types of satellite in the same
manner. The analysis of their rotation is done in a non-canonical Hamiltonian
formalism closely related to Poincare's "forme nouvelle des equations de la
mecanique". In the case of a satellite with a global ocean, we obtain a
seven-degree of freedom system. Six of them account for the motion of the two
rigid components, and the last one is associated with the fluid layer. We apply
our model to Titan for which the origin of the obliquity is still a debated
question. We show that the observed value is compatible with Titan slightly
departing from the hydrostatic equilibrium and being in a Cassini equilibrium
state.
