Geometric description of vakonomic and nonholonomic dynamics. Comparison of solutions

We treat the vakonomic dynamics with general constraints within a new geometric framework, which can be useful in the study of optimal control problems. We compare our formulation with the one of Vershik and Gershkovich in the case of linear constraints. We show how nonholonomic mechanics also admits a new geometrical description which allows us to develop an algorithm of comparison between the solutions of both dynamics. Examples illustrating the theory are treated.