Momentum map reduction for nonholonomic systems
Mathematical Physics
2022-07-07 v1 Differential Geometry
math.MP
Abstract
This paper presents a reduction procedure for nonholonomic systems admitting suitable types of symmetries and conserved quantities. The full procedure contains two steps. The first (simple) step results in a Chaplygin system, described by an almost symplectic structure, carrying additional symmetries. The focus of this paper is on the second step, which consists of a Marsden-Weinstein--type reduction that generalizes constructions in [4,17]. The almost symplectic manifolds obtained in the second step are proven to coincide with the leaves of the reduced nonholonomic brackets defined in [7]. We illustrate our construction with several classical examples.
Keywords
Cite
@article{arxiv.2207.02251,
title = {Momentum map reduction for nonholonomic systems},
author = {Paula Balseiro and Maria E. Garcia and Cora Tori and Marcela Zuccalli},
journal= {arXiv preprint arXiv:2207.02251},
year = {2022}
}