Lagrangian Mechanics and Reduction on Fibered Manifolds
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 action...
Saved in:
| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2017 |
| Main Authors: | , , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2017
|
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/148564 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| 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. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862536323481468928 |
|---|---|
| author | Li, S. Stern, A. Tang, X. |
| author_facet | Li, S. Stern, A. Tang, X. |
| citation_txt | 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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.
|
| first_indexed | 2025-11-24T11:04:38Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-148564 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-24T11:04:38Z |
| publishDate | 2017 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Li, S. Stern, A. Tang, X. 2019-02-18T15:53:08Z 2019-02-18T15:53:08Z 2017 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. 1815-0659 2010 Mathematics Subject Classification: 70G45; 53D17; 37J15 DOI:10.3842/SIGMA.2017.019 https://nasplib.isofts.kiev.ua/handle/123456789/148564 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. The authors wish to thank Rui Loja Fernandes for his helpful feedback on this work. This paper
 also benefited substantially from the suggestions of the anonymous referees, to whom we wish to
 express our sincere gratitude. This research was supported in part by grants from the Simons
 Foundation (award 279968 to Ari Stern) and from the National Science Foundation (award
 DMS 1363250 to Xiang Tang). The authors declare that they have no conflict of interest. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Lagrangian Mechanics and Reduction on Fibered Manifolds Article published earlier |
| spellingShingle | Lagrangian Mechanics and Reduction on Fibered Manifolds Li, S. Stern, A. Tang, X. |
| title | Lagrangian Mechanics and Reduction on Fibered Manifolds |
| title_full | Lagrangian Mechanics and Reduction on Fibered Manifolds |
| title_fullStr | Lagrangian Mechanics and Reduction on Fibered Manifolds |
| title_full_unstemmed | Lagrangian Mechanics and Reduction on Fibered Manifolds |
| title_short | Lagrangian Mechanics and Reduction on Fibered Manifolds |
| title_sort | lagrangian mechanics and reduction on fibered manifolds |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/148564 |
| work_keys_str_mv | AT lis lagrangianmechanicsandreductiononfiberedmanifolds AT sterna lagrangianmechanicsandreductiononfiberedmanifolds AT tangx lagrangianmechanicsandreductiononfiberedmanifolds |