Geometric description of vakonomic and nonholonomic dynamics. Comparison of solutions

2000/06/24 by Jorge Cortes, Manuel de Leon, David Martin de Diego +1 · 1 citation
Mathematics · #math.DG #math.OC #math.SG #msc:34A26 #msc:49K15 #msc:70F25

paper · pdf

published as SIAM J Control Optim 41 (5) (2003), 1389-1412 · 34 pages

arxiv created 2000/06/24 · arxiv updated 2009/11/30

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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• Integrable Non-Holonomic Constraints and Gauge Fixing in Classical Field Theory

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