On the geometry of discrete contact mechanics

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.Manuel Lainz wishes to thank MICINN and ICMAT for a FPI-Severo Ochoa predoctoral contract PRE2018-083203. The authors are supported by Ministerio de Ciencia e Innovación (Spain) under Grants PID2019-106715GB-C21, MTM2016-76702-P and “Severo Ochoa Programme for Centres of Excellence” in R&D (SEV-2015-0554). A. Simoes is supported by the FCT (Portugal) research fellowship SFRH/BD/129882/2017 partially funded by the European Union (ESF). M. Lainz wishes to thank MICINN and ICMAT for a FPI-Severo Ochoa predoctoral contract PRE2018-083203