Lagrangian Mechanics and Reduction on Fibered Manifolds

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2017
• Main Authors: Li, S., Stern, A., Tang, X.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2017
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/148564
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Lagrangian Mechanics and Reduction on Fibered Manifolds / S. Li, A. Stern, X. Tang // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 34 назв. — англ.

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.