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This article is cited in 3 scientific papers (total in 3 papers)
Lagrangian Mechanics and Reductionon Fibered Manifolds
Songhao Li, Ari Stern, Xiang Tang Department of Mathematics, Washington University in St. Louis, One Brookings Drive, St. Louis MO 63130-4899, USA
Abstract:
This paper develops a generalized formulation of Lagrangian mechanics on fibered manifolds, together with a reduction theory for symmetries corresponding to Lie groupoid actions. As special cases, this theory includes not only Lagrangian reduction (including reduction by stages) for Lie group actions, but also classical Routh reduction, which we show is naturally posed in this fibered setting. Along the way, we also develop some new results for Lagrangian mechanics on Lie algebroids, most notably a new, coordinate-free formulation of the equations of motion. Finally, we extend the foregoing to include fibered and Lie algebroid generalizations of the Hamilton–Pontryagin principle of Yoshimura and Marsden, along with the associated reduction theory.
Keywords:
Lagrangian mechanics; reduction; fibered manifolds; Lie algebroids; Lie groupoids.
Received: October 5, 2016; in final form March 13, 2017; Published online March 22, 2017
Citation:
Songhao Li, Ari Stern, Xiang Tang, “Lagrangian Mechanics and Reductionon Fibered Manifolds”, SIGMA, 13 (2017), 019, 26 pp.
Linking options:
https://www.mathnet.ru/eng/sigma1219 https://www.mathnet.ru/eng/sigma/v13/p19
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Abstract page: | 191 | Full-text PDF : | 32 | References: | 32 |
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