Geometric description of vakonomic and nonholonomic dynamics. Comparison of solutions

We treat the vakonomic dynamics with general constraints within a new geometric framework which will be appropriate to study optimal control problems. We compare our formulation with Vershik-Gershkovich one in the case of linear constraints. We show how nonholonomic mechanics also admits a new geometrical description wich enables us to develop an algorithm of comparison between the solutions of both dynamics. Some examples illustrating the theory are treated.