Numerical integration in Celestial Mechanics: a case for contact geometry

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.