In this paper, we continue the construction of variational integrators adapted to contact geometry started in Vermeeren et al. (J Phys A 52(44):445206, 2019), 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

在本文中，我们将继续构建适用于Vermeeren等人的接触几何的变分积分器。（J Phys A 52（44）：445206，2019），特别是，我们引入了离散Herglotz原理以及接触设置中离散Lagrangian的相应离散Herglotz方程。这使我们能够为构造上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。