Lagrangian Mechanics and Reduction on Fibered Manifolds

Symmetry Integrability and Geometry-Methods and Applications

article

Songhao Li¹  Ari Stern¹  Xiang Tang¹ 

[1] Department of Mathematics, Washington University in St. Louis

关键词: Lagrangian mechanics;    reduction;    fibered manifolds;    Lie algebroids;    Lie groupoids;   

DOI  :  10.3842/SIGMA.2017.019

来源: National Academy of Science of Ukraine

【 摘 要 】

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.

【 授权许可】

Unknown