2022/07/05 by Balseiro, Paula, Garcia, Maria E., Tori, Cora +1
#53D20 #70F25 #70G45 #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.2207.02251
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.