Juan Carlos Marrero  (Universidad de La Laguna, Spain)

Kinetic nonholonomic dynamics is neither Hamiltonian nor variational and however...

Abstract:
It is well-known that kinetic nonholonomic dynamics is neither Hamiltonian nor variational. However, in this talk, after introducing a geometrical description of nonholonomic dynamics, I will present a result which is a little surprising. Namely, for a kinetic nonholonomic system and a given point q of the configuration space Q, one may define:

(1) A submanifold of Q, which contains to the point q and whose dimension is equal to the rank of the constraint distribution, and

(2)  A family of Riemannian metrics on the submanifold such that the geodesics of these metrics  starting at  q are just the nonholonomic trajectories starting at q.

In particular, the previous facts imply that the previous nonholonomic trajectories, for sufficiently small times, minimize length in the submanifold defined in (1).