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Geometric description of vakonomic and nonholonomic dynamics. Comparison of solutions

Jorge Cortes·Manuel de Leon·David Martin de Diego·Sonia Martinez
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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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Jorge Cortes, Manuel de Leon, David Martin de Diego, Sonia Martinez. 2000-06-24. Geometric description of vakonomic and nonholonomic dynamics. Comparison of solutions. https://arxiv.org/abs/math/0006183

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