Momentum map reduction for nonholonomic systems

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 symmetrie...

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Bibliographic Details
Published in:Nonlinearity 2023-10, Vol.36 (10), p.5401-5421
Main Authors: Balseiro, Paula, Eugenia Garcia, Maria, Tori, Cora Inés, Zuccalli, Marcela
Format: Article
Language:English
Subjects:
(almost) symplectic reduction
53D20
70F25
70G45
first integrals
geometric mechanics
momentum maps
nonholonomic systems
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Summary: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 generalises constructions in (Balseiro and Fernandez 2015 Nonlinearity 28 2873–912, Cortés Monforte 2002 Geometric, Control and Numerical Aspects of non-Holonomic Systems (Springer)). The almost symplectic manifolds obtained in the second step are proven to coincide with the leaves of the reduced nonholonomic brackets defined in (Balseiro and Yapu-Quispe 2021 Ann. Inst. Henri Poincare C 38 23–60). We illustrate our construction with several classical examples.
ISSN:0951-7715
1361-6544
DOI:10.1088/1361-6544/acecf3