In this paper, we continue the construction of variational integrators adapted to contact geometry started in \cite{VBS}, in particular, we introduce a discrete Herglotz Principle and the corresponding discrete Herglotz Equations for a discrete Lagrangian in the contact setting. This allows us to develop convenient numerical integrators for contact Lagrangian systems that are conformally contact by construction. The existence of an exact Lagrangian function is also discussed.

中文翻译：

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离散接触力学的几何学

在本文中，我们继续构建适用于从 \cite{VBS} 开始的接触几何的变分积分器，特别是，我们在接触设置中引入了离散 Herglotz 原理和相应的离散拉格朗日方程的离散 Herglotz 方程。这使我们能够为通过构造共形接触的接触拉格朗日系统开发方便的数值积分器。还讨论了精确拉格朗日函数的存在。