TL;DR
This paper explores the application of contact geometry to celestial mechanics models, aiming to develop geometric integrators for systems with time-dependent damping, such as the modified Kepler problem and spin-orbit models.
Contribution
It introduces a contact geometric framework for celestial mechanics models with damping and proposes methods for geometric integration of these systems.
Findings
Contact Hamiltonisation of celestial models
Construction of geometric integrators for damped systems
Potential improvements in numerical stability and accuracy
Abstract
Several dynamical systems of interest in celestial mechanics can be written in the form of a Newton equation with time-dependent damping, linear in the velocities. For instance, the modified Kepler problem, the spin-orbit model and the Lane-Emden equation all belong to such class. In this work we start an investigation of these models from the point of view of contact geometry. In particular we focus on the (contact) Hamiltonisation of these models and on the construction of the corresponding geometric integrators.
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