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.

中文翻译：

---

天体力学中的数值积分：以接触几何为例

天体力学中感兴趣的几个动力系统可以写成牛顿方程的形式，其阻尼随时间变化，速度呈线性。例如，修正开普勒问题、自旋轨道模型和莱恩-埃姆登方程都属于此类。在这项工作中，我们从接触几何的角度开始研究这些模型。特别是，我们关注这些模型的（接触）哈密顿化以及相应几何积分器的构造。