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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| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Datum: | 2016 |
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| Format: | Artikel |
| Sprache: | English |
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Інститут математики НАН України
2016
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/148551 |
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| Zitieren: | 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. |
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García-Toraño Andrés, E. Mestdag, T. 2019-02-18T15:23:16Z 2019-02-18T15:23:16Z 2016 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 https://nasplib.isofts.kiev.ua/handle/123456789/148551 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. EGTA thanks the CONICET for financial support through a Postdoctoral Grant. TM is a visiting professor at Ghent University: he is grateful to the Department of Mathematics for its hospitality. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Un-Reduction of Systems of Second-Order Ordinary Differential Equations Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Un-Reduction of Systems of Second-Order Ordinary Differential Equations |
| spellingShingle |
Un-Reduction of Systems of Second-Order Ordinary Differential Equations García-Toraño Andrés, E. Mestdag, T. |
| 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 |
| author |
García-Toraño Andrés, E. Mestdag, T. |
| author_facet |
García-Toraño Andrés, E. Mestdag, T. |
| publishDate |
2016 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| 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.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.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. |
| work_keys_str_mv |
AT garciatoranoandrese unreductionofsystemsofsecondorderordinarydifferentialequations AT mestdagt unreductionofsystemsofsecondorderordinarydifferentialequations |
| first_indexed |
2025-12-07T18:44:02Z |
| last_indexed |
2025-12-07T18:44:02Z |
| _version_ |
1850876145694670848 |