Integrators for Nonholonomic Mechanical Systems

We study a discrete analog of the Lagrange-d’Alembert principle of nonhonolomic mechanics and give conditions for it to define a map and to be reversible. In specific cases it can generate linearly implicit, semi-implicit, or implicit numerical integrators for nonholonomic systems which, in several examples, exhibit superior preservation of the dynamics. We also study discrete nonholonomic systems on Lie groups and their reduction theory, and explore the properties of the exact discrete flow of a nonholonomic system.