Exact discrete Lagrangian mechanics for nonholonomic mechanics

We construct the exponential map associated to a nonholonomic system that allows us to define an exact discrete nonholonomic constraint submanifold. We reproduce the continuous nonholonomic flow as a discrete flow on this discrete constraint submanifold deriving an exact discrete version of the nonholonomic equations. Finally, we derive a general family of nonholonomic integrators that includes as a particular case the exact discrete nonholonomic trajectoryD. Martín de Diego and A. Simoes acknowledge financial support from the Spanish Ministry of Science and Innovation, under grants PID2019-106715GB-C21, MTM2016-76702-P, and from the Spanish National Research Council, through the “Ayuda extraordinaria a Centros de Excelencia Severo Ochoa” R&D (CEX2019-000904-S). A. Simoes is supported by the FCT research fellowship SFRH/BD/129882/2017 partially funded by the European Union (ESF). J.C. Marrero acknowledges the partial support by European Union (Feder) grant MTM 2015-64166-C2-2P and PGC2018-098265-B-C32