Structure-Preserving Integrators for Nonholonomic Systems

Nonholonomic systems are mechanical systems subject to velocity
constraints, such as rolling and/or sliding contacts. There are some
fascinating differences between nonholonomic systems and classical
Hamiltonian or Lagrangian systems. In particular, momentum is not
always preserved in systems with symmetry, and, unlike the Hamiltonian
setting, volume may not be preserved in the phase space, leading to
interesting asymptotic stability of relative equilibria, despite
energy conservation. Nonholonomic integrators are discrete-time
analogues of nonholonomic mechanical systems obtained by discretizing
the Lagrange-d'Alembert variational principle. The symmetry-induced
structure-preserving properties of these integrators, such as momentum
conservation and preservation of geometry of manifolds of relative
equilibria and their stability type, will be discussed.