Un-Reduction of Systems of Second-Order Ordinary Differential Equations
In this paper we consider an alternative approach to ''un-reduction''. This is the process where one associates to a Lagrangian system on a manifold a dynamical system on a principal bundle over that manifold, in such a way that solutions project. We show that, when written in te...
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| Видавець: | Інститут математики НАН України |
|---|---|
| Дата: | 2016 |
| Автори: | , |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут математики НАН України
2016
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/148551 |
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| Цитувати: | Un-Reduction of Systems of Second-Order Ordinary Differential Equations / E. García-Toraño Andrés, T. Mestdag // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 19 назв. — англ. |
Репозиторії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-148551 |
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irk-123456789-1485512019-02-19T01:24:07Z Un-Reduction of Systems of Second-Order Ordinary Differential Equations García-Toraño Andrés, E. Mestdag, T. In this paper we consider an alternative approach to ''un-reduction''. This is the process where one associates to a Lagrangian system on a manifold a dynamical system on a principal bundle over that manifold, in such a way that solutions project. We show that, when written in terms of second-order ordinary differential equations (SODEs), one may associate to the first system a (what we have called) ''primary un-reduced SODE'', and we explain how all other un-reduced SODEs relate to it. We give examples that show that the considered procedure exceeds the realm of Lagrangian systems and that relate our results to those in the literature. 2016 Article Un-Reduction of Systems of Second-Order Ordinary Differential Equations / E. García-Toraño Andrés, T. Mestdag // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 19 назв. — англ. 1815-0659 2010 Mathematics Subject Classification: 34A26; 37J15; 70H33; 70G65 DOI:10.3842/SIGMA.2016.115 http://dspace.nbuv.gov.ua/handle/123456789/148551 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 |
In this paper we consider an alternative approach to ''un-reduction''. This is the process where one associates to a Lagrangian system on a manifold a dynamical system on a principal bundle over that manifold, in such a way that solutions project. We show that, when written in terms of second-order ordinary differential equations (SODEs), one may associate to the first system a (what we have called) ''primary un-reduced SODE'', and we explain how all other un-reduced SODEs relate to it. We give examples that show that the considered procedure exceeds the realm of Lagrangian systems and that relate our results to those in the literature. |
| format |
Article |
| author |
García-Toraño Andrés, E. Mestdag, T. |
| spellingShingle |
García-Toraño Andrés, E. Mestdag, T. Un-Reduction of Systems of Second-Order Ordinary Differential Equations Symmetry, Integrability and Geometry: Methods and Applications |
| author_facet |
García-Toraño Andrés, E. Mestdag, T. |
| author_sort |
García-Toraño Andrés, E. |
| title |
Un-Reduction of Systems of Second-Order Ordinary Differential Equations |
| title_short |
Un-Reduction of Systems of Second-Order Ordinary Differential Equations |
| title_full |
Un-Reduction of Systems of Second-Order Ordinary Differential Equations |
| title_fullStr |
Un-Reduction of Systems of Second-Order Ordinary Differential Equations |
| title_full_unstemmed |
Un-Reduction of Systems of Second-Order Ordinary Differential Equations |
| title_sort |
un-reduction of systems of second-order ordinary differential equations |
| publisher |
Інститут математики НАН України |
| publishDate |
2016 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/148551 |
| citation_txt |
Un-Reduction of Systems of Second-Order Ordinary Differential Equations / E. García-Toraño Andrés, T. Mestdag // Symmetry, Integrability and Geometry: Methods and Applications. — 2016. — Т. 12. — Бібліогр.: 19 назв. — англ. |
| series |
Symmetry, Integrability and Geometry: Methods and Applications |
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AT garciatoranoandrese unreductionofsystemsofsecondorderordinarydifferentialequations AT mestdagt unreductionofsystemsofsecondorderordinarydifferentialequations |
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2023-05-20T17:29:43Z |
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2023-05-20T17:29:43Z |
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