Hamiltonian formulation of the spin-orbit model with time-varying non-conservative forces

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.