  In a realistic scenario, the evolution of the rotational dynamics of a
celestial or artificial body is subject to dissipative effects. Time-varying
non-conservative forces can be due to, for example, a variation of the moments
of inertia or to tidal interactions. In this work, we consider a simplified
model describing the rotational dynamics, known as the spin-orbit problem,
where we assume that the orbital motion is provided by a fixed Keplerian
ellipse. We consider different examples in which a non-conservative force acts
on the model and we propose an analytical method, which reduces the system to a
Hamiltonian framework. In particular, we compute a time parametrisation in a
series form, which allows us to transform the original system into a
Hamiltonian one. We also provide applications of our method to study the
rotational motion of a body with time-varying moments of inertia, e.g. an
artificial satellite with flexible components, as well as subject to a tidal
torque depending linearly on the velocity.
