  Perturbations of all sorts destabilise the rotation of a small body and leave
it in a non-principal spin state. In such a state, the body experiences
alternating stresses generated by the inertial forces. This yields nutation
relaxation, i.e., evolution of the spin towards the principal rotation about
the maximal-inertia axis. Knowledge of the timescales needed to damp the
nutation is crucial in studies of small bodies' dynamics. In the literature
hitherto, nutation relaxation has always been described with aid of an
empirical quality factor $\,Q\,$ introduced to parameterise the energy
dissipation rate.
  Among the drawbacks of this approach was its inability to describe the
dependence of the relaxation rate upon the current nutation angle. This
inability stemmed from our lack of knowledge of the quality factor's dependence
on the forcing frequency. In this article, we derive our description of
nutation damping directly from the rheological law obeyed by the material. This
renders us the nutation damping rate as a function of the current nutation
angle, as well as of the shape and the rheological parameters of the body. In
contradistinction from the approach based on an empirical $\,Q\,$-factor, our
development gives a zero damping rate in the spherical-shape limit. Our method
is generic and applicable to any shape and to any linear rheological law.
However, to simplify the developments, here we consider a dynamically oblate
rotator with a Maxwell rheology.
