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In this paper, we propose a geometric integrator for nonholonomic mechanicalsystems. It can be applied to discrete Lagrangian systems specified through adiscrete Lagrangian defined on QxQ, where Q is the configuration manifold, anda (generally nonintegrable) distribution in TQ. In the proposed method, adiscretization of the constraints is not required. We show that the methodpreserves the discrete nonholonomic momentum map, and also that thenonholonomic constraints are preserved in average. We study in particular thecase where Q has a Lie group structure and the discrete Lagrangian and/ornonholonomic constraints have various invariance properties, and show that themethod is also energy-preserving in some important cases.

Momentum and energy preserving integrators for nonholonomic dynamics