Geometric description of vakonomic and nonholonomic dynamics. Comparison of solutions

Details Geometric description of vakonomic and nonholonomic dynamics. Comparison of solutions Geometric description of vakonomic and nonholonomic dynamics. Comparison of solutions

2000-06-24

arxiv.org/abs/math/0006183v1

SIAM J Control Optim 41 (5) (2003), 1389-1412

Mathematics

Differential Geometry

34 pages

Scientific paper

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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