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

## TL;DR

This paper develops a Hamiltonian framework for the spin-orbit problem with time-varying non-conservative forces, enabling analytical study of rotational dynamics in celestial and artificial bodies with dissipative effects.

## Contribution

It introduces a novel analytical method to transform non-conservative spin-orbit models into Hamiltonian systems using a series-based time parametrization.

## Key findings

- Successfully applied to bodies with varying moments of inertia.
- Effectively models tidal torques depending on velocity.
- Provides a new tool for analyzing dissipative rotational dynamics.

## Abstract

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.