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arXiv · 2207.02251

Momentum map reduction for nonholonomic systems

Paula Balseiro·Maria E. Garcia·Cora Tori·Marcela Zuccalli
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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.

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Paula Balseiro, Maria E. Garcia, Cora Tori, Marcela Zuccalli. 2022-07-05. Momentum map reduction for nonholonomic systems. https://arxiv.org/abs/2207.02251

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