  We present fully three-dimensional equations to describe the rotations of a
body made of a deformable mantle and a fluid core. The model in its essence is
similar to that used by INPOP (Integration Plan\'{e}taire de l'Observatoire de
Paris), e.g. Viswanathan et al. (2019), and by JPL (Jet Propulsion Laboratory),
e.g. Folkner et al. (2014), to represent the Moon. The intended advantages of
our model are: straightforward use of any linear-viscoelastic model for the
rheology of the mantle; easy numerical implementation in time-domain (no time
lags are necessary); all parameters, including those related to the "permanent
deformation", have a physical interpretation. The paper also contains: 1) A
physical model to explain the usual lack of hydrostaticity of the mantle
(permanent deformation). 2) Formulas for free librations of bodies in and
out-of spin-orbit resonance that are valid for any linear viscoelastic rheology
of the mantle. 3) Formulas for the offset between the mantle and the idealized
rigid-body motion (Peale's Cassini states). 4) Applications to the librations
of Moon, Earth, and Mercury that are used for model validation.
