Geometric description of vakonomic and nonholonomic dynamics. Comparison of solutions
Jorge Cortes, Manuel de Leon, David Martin de Diego, Sonia Martinez
Abstract
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.
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