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