A momentum-energy integrator for nonholonomic dynamics

SEBASTIÁN J. FERRARO; DAVID IGLESIAS-PONTE; DAVID MARTÍN DE DIEGO

Lisboa, Portugal

Workshop; IFWGP '07, XIV International Fall Workshop on Geometry and Physics; 2007

We propose a geometric integrator for nonholonomic mechanical systems. It can be applied to discrete Lagrangian systems specified through a discrete Lagrangian L_d: Q×Q->R, where Q is the configuration manifold, and a (generally nonintegrable) distribution D \subset TQ representing linear constraints on the continuous velocities. In the proposed method, a discretization of the constraints is not required. We show that the method preserves the discrete nonholonomic momentum map in the presence of horizontal symmetries, and also that the nonholonomic constraints are preserved in average.We study in particular the case where Q has a Lie group structure and the discrete Lagrangian and/or nonholonomic constraints have various invariance properties, and we show that the method is also energy-preserving in some important cases.