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. 
Jorge Cortes, Manuel de Leon, David Martin de Diego and Sonia Martinez