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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| Дата: | 2011 |
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| Автори: | , , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2011
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/148086 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | Routh Reduction by Stages / B. Langerock, T. Mestdag, J. Vankerschaver // Symmetry, Integrability and Geometry: Methods and Applications. — 2011. — Т. 7. — Бібліогр.: 20 назв. — англ. |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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irk-123456789-1480862019-02-17T01:27:41Z 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. 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 http://dspace.nbuv.gov.ua/handle/123456789/148086 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
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 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/148086 |
| 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 |
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AT langerockb routhreductionbystages AT mestdagt routhreductionbystages AT vankerschaverj routhreductionbystages |
| first_indexed |
2023-05-20T17:28:54Z |
| last_indexed |
2023-05-20T17:28:54Z |
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1796153399316578304 |