We study the existence of first integrals in nonholonomic systems with symmetry. First we define the concept of M -cotangent lift of a vector field on a manifold Q in order to unify the works [Balseiro P., Arch. Ration. Mech. Anal. 214 (2014), 453-501, arXiv:1301.1091], [Fosse F., Ramos A., Sansonetto N., Regul. Chaotic Dyn. 12 (2007), 579588], and [Fosse F., Giacobbe A., Sansonetto N., Rep. Math. Phys. 62 (2008), 345-367]. Second, we study gauge symmetries and gauge momenta, in the cases in which there are the symmetries that satisfy the so-called vertical symmetry condition. Under such condition we can predict the number of linearly independent first integrals (that are gauge momenta). We illustrate the theory with two examples.

A Geometric Characterization of Certain First Integrals for Nonholonomic Systems with Symmetries

Sansonetto, Nicola
2016-01-01

Abstract

We study the existence of first integrals in nonholonomic systems with symmetry. First we define the concept of M -cotangent lift of a vector field on a manifold Q in order to unify the works [Balseiro P., Arch. Ration. Mech. Anal. 214 (2014), 453-501, arXiv:1301.1091], [Fosse F., Ramos A., Sansonetto N., Regul. Chaotic Dyn. 12 (2007), 579588], and [Fosse F., Giacobbe A., Sansonetto N., Rep. Math. Phys. 62 (2008), 345-367]. Second, we study gauge symmetries and gauge momenta, in the cases in which there are the symmetries that satisfy the so-called vertical symmetry condition. Under such condition we can predict the number of linearly independent first integrals (that are gauge momenta). We illustrate the theory with two examples.
nonholonomic systems; Lie group symmetries; first integrals; gauge symmetries; and gauge momenta
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11562/1009286
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