Lie Algebroids in Classical Mechanics and Optimal Control
We review some recent results on the theory of Lagrangian systems on Lie algebroids. In particular we consider the symplectic and variational formalism and we study reduction. Finally we also consider optimal control systems on Lie algebroids and we show how to reduce Pontryagin maximum principle.
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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Datum: | 2007 |
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут математики НАН України
2007
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/147813 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Lie Algebroids in Classical Mechanics and Optimal Control / E. Martínez // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 25 назв. — англ. |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862696478190862336 |
|---|---|
| author | Martínez, E. |
| author_facet | Martínez, E. |
| citation_txt | Lie Algebroids in Classical Mechanics and Optimal Control / E. Martínez // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 25 назв. — англ. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | We review some recent results on the theory of Lagrangian systems on Lie algebroids. In particular we consider the symplectic and variational formalism and we study reduction. Finally we also consider optimal control systems on Lie algebroids and we show how to reduce Pontryagin maximum principle.
|
| first_indexed | 2025-12-07T16:27:22Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-147813 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-07T16:27:22Z |
| publishDate | 2007 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Martínez, E. 2019-02-16T08:39:09Z 2019-02-16T08:39:09Z 2007 Lie Algebroids in Classical Mechanics and Optimal Control / E. Martínez // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 25 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 49S05; 70H25; 22A22; 49J15 https://nasplib.isofts.kiev.ua/handle/123456789/147813 We review some recent results on the theory of Lagrangian systems on Lie algebroids. In particular we consider the symplectic and variational formalism and we study reduction. Finally we also consider optimal control systems on Lie algebroids and we show how to reduce Pontryagin maximum principle. This paper is a contribution to the Proceedings of the Workshop on Geometric Aspects of Integrable Systems (July 17–19, 2006, University of Coimbra, Portugal). Partial financial support from MEC-DGI (Spain) grants BFM 2003-02532 and MTM2006-10531 is acknowledged. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Lie Algebroids in Classical Mechanics and Optimal Control Article published earlier |
| spellingShingle | Lie Algebroids in Classical Mechanics and Optimal Control Martínez, E. |
| title | Lie Algebroids in Classical Mechanics and Optimal Control |
| title_full | Lie Algebroids in Classical Mechanics and Optimal Control |
| title_fullStr | Lie Algebroids in Classical Mechanics and Optimal Control |
| title_full_unstemmed | Lie Algebroids in Classical Mechanics and Optimal Control |
| title_short | Lie Algebroids in Classical Mechanics and Optimal Control |
| title_sort | lie algebroids in classical mechanics and optimal control |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/147813 |
| work_keys_str_mv | AT martineze liealgebroidsinclassicalmechanicsandoptimalcontrol |