Routh Reduction by Stages
This paper deals with the Lagrangian analogue of symplectic or point reduction by stages. We develop Routh reduction as a reduction technique that preserves the Lagrangian nature of the dynamics. To do so we heavily rely on the relation between Routh reduction and cotangent symplectic reduction. The...
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| Date: | 2011 |
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Інститут математики НАН України
2011
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| Series: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Cite this: | Routh Reduction by Stages / B. Langerock, T. Mestdag, J. Vankerschaver // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 20 назв. — англ. |
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oai:nasplib.isofts.kiev.ua:123456789-1480862025-02-23T17:29:50Z Routh Reduction by Stages Langerock, B. Mestdag, T. Vankerschaver, J. This paper deals with the Lagrangian analogue of symplectic or point reduction by stages. We develop Routh reduction as a reduction technique that preserves the Lagrangian nature of the dynamics. To do so we heavily rely on the relation between Routh reduction and cotangent symplectic reduction. The main results in this paper are: (i) we develop a class of so called magnetic Lagrangian systems and this class has the property that it is closed under Routh reduction; (ii) we construct a transformation relating the magnetic Lagrangian system obtained after two subsequent Routh reductions and the magnetic Lagrangian system obtained after Routh reduction w.r.t. to the full symmetry group. BL is an honorary postdoctoral researcher at the Department of Mathematics of Ghent University and associate academic staf f at the Department of Mathematics of K.U.Leuven. BL is sponsored by a Research Programme of the Research Foundation – Flanders (FWO). Part of this work was supported by the Sint-Lucas department of Architecture, K.U.Leuven Association. TM is a Postdoctoral Fellow of the Research Foundation – Flanders (FWO). JV is a postdoc at the Department of Mathematics of UC San Diego, partially supported by NSF CAREER award DMS-1010687 and NSF FRG grant DMS-1065972, and is on leave from a Postdoctoral Fellowship of the Research Foundation–Flanders. This work is part of the irses project geomech (nr. 246981) within the 7th European Community Framework Programme. We are indebted to F. Cantrijn, M. Crampin and E. Garc´ıa-Tora˜no Andres for many useful discussions. We thank one of the referees for pointing out reference [16] on the reduction hypothesis. 2011 Article Routh Reduction by Stages / B. Langerock, T. Mestdag, J. Vankerschaver // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 20 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 37J05; 37J15; 52D20 DOI: http://dx.doi.org/10.3842/SIGMA.2011.109 https://nasplib.isofts.kiev.ua/handle/123456789/148086 en Symmetry, Integrability and Geometry: Methods and Applications application/pdf Інститут математики НАН України |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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English |
| description |
This paper deals with the Lagrangian analogue of symplectic or point reduction by stages. We develop Routh reduction as a reduction technique that preserves the Lagrangian nature of the dynamics. To do so we heavily rely on the relation between Routh reduction and cotangent symplectic reduction. The main results in this paper are: (i) we develop a class of so called magnetic Lagrangian systems and this class has the property that it is closed under Routh reduction; (ii) we construct a transformation relating the magnetic Lagrangian system obtained after two subsequent Routh reductions and the magnetic Lagrangian system obtained after Routh reduction w.r.t. to the full symmetry group. |
| format |
Article |
| author |
Langerock, B. Mestdag, T. Vankerschaver, J. |
| spellingShingle |
Langerock, B. Mestdag, T. Vankerschaver, J. Routh Reduction by Stages Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
Langerock, B. Mestdag, T. Vankerschaver, J. |
| author_sort |
Langerock, B. |
| title |
Routh Reduction by Stages |
| title_short |
Routh Reduction by Stages |
| title_full |
Routh Reduction by Stages |
| title_fullStr |
Routh Reduction by Stages |
| title_full_unstemmed |
Routh Reduction by Stages |
| title_sort |
routh reduction by stages |
| publisher |
Інститут математики НАН України |
| publishDate |
2011 |
| citation_txt |
Routh Reduction by Stages / B. Langerock, T. Mestdag, J. Vankerschaver // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 20 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
| work_keys_str_mv |
AT langerockb routhreductionbystages AT mestdagt routhreductionbystages AT vankerschaverj routhreductionbystages |
| first_indexed |
2025-07-22T04:20:43Z |
| last_indexed |
2025-07-22T04:20:43Z |
| _version_ |
1838319449467256832 |