A Geometric Characterization of Certain First Integrals for Nonholonomic Systems with Symmetries
Dynamical Systems
2016-02-23 v2 Mathematical Physics
math.MP
Symplectic Geometry
Abstract
We study the existence of first integrals in nonholonomic systems with symmetry. First we define the concept of -cotangent lift of a vector field on a manifold in order to unify the works [Balseiro P., Arch. Ration. Mech. Anal. 214 (2014), 453-501, arXiv:1301.1091], [Fass\`o F., Ramos A., Sansonetto N., Regul. Chaotic Dyn. 12 (2007), 579-588], and [Fass\`o 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.
Keywords
Cite
@article{arxiv.1510.08314,
title = {A Geometric Characterization of Certain First Integrals for Nonholonomic Systems with Symmetries},
author = {Paula Balseiro and Nicola Sansonetto},
journal= {arXiv preprint arXiv:1510.08314},
year = {2016}
}