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Эта публикация цитируется в 3 научных статьях (всего в 3 статьях)
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
Аннотация:
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.
Ключевые слова:
Lagrangian mechanics; reduction; fibered manifolds; Lie algebroids; Lie groupoids.
Поступила: 5 октября 2016 г.; в окончательном варианте 13 марта 2017 г.; опубликована 22 марта 2017 г.
Образец цитирования:
Songhao Li, Ari Stern, Xiang Tang, “Lagrangian Mechanics and Reductionon Fibered Manifolds”, SIGMA, 13 (2017), 019, 26 pp.
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/sigma1219 https://www.mathnet.ru/rus/sigma/v13/p19
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