Discrete Mechanics and Nonholonomic Integrators

Nonholonomic systems are mechanical systems with ideal linear velocity constraints that are not derivable from position constraints and with dynamics identified by the Lagrange – d’Alembert principle. This paper surveys discrete-time nonholonomic mechanics with applications to numerical integration of nonholonomic systems. This includes an exposition of key elements of discrete mechanics, discrete Lagrange – d’Alembert principle, and exact nonholonomic integrators on vector spaces. Exact variational integrators were introduced and exposed in the context of Lagrangian mechanics by Marsden and West. These integrators sample the trajectories of mechanical systems and are useful for developing practical mechanical integrators.