Tulczyjew’s triplet for lie groups III: Higher order dynamics and reductions for iterated bundles
Given a Lie group 𝐺, we elaborate the dynamics on 𝑇*𝑇*𝐺 and 𝑇*𝑇𝐺, which is given by a Hamiltonian, as well as the dynamics on the Tulczyjew symplectic space 𝑇𝑇*𝐺, which may be defined by a Lagrangian or a Hamiltonian function. As the trivializations we adapted respect the group structures of the ite...
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| Format: | Article |
| Language: | English |
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Serbian Society of Mechanics & Mathematical Institute of the Serbian Academy of Sciences and Arts, Belgrade
2021-01-01
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| Series: | Theoretical and Applied Mechanics |
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| Online Access: | http://www.doiserbia.nb.rs/img/doi/1450-5584/2021/1450-55842100009E.pdf |
| _version_ | 1818284847831973888 |
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| author | Esen Oğul Gümral Hasan Sütlü Serkan |
| author_facet | Esen Oğul Gümral Hasan Sütlü Serkan |
| author_sort | Esen Oğul |
| collection | DOAJ |
| description | Given a Lie group 𝐺, we elaborate the dynamics on 𝑇*𝑇*𝐺 and 𝑇*𝑇𝐺, which is given by a Hamiltonian, as well as the dynamics on the Tulczyjew symplectic space 𝑇𝑇*𝐺, which may be defined by a Lagrangian or a Hamiltonian function. As the trivializations we adapted respect the group structures of the iterated bundles, we exploit all possible subgroup reductions (Poisson, symplectic or both) of higher order dynamics. |
| first_indexed | 2024-12-13T00:59:19Z |
| format | Article |
| id | doaj.art-6b2d3d6e52274233b1d96f8333c5d655 |
| institution | Directory Open Access Journal |
| issn | 1450-5584 2406-0925 |
| language | English |
| last_indexed | 2024-12-13T00:59:19Z |
| publishDate | 2021-01-01 |
| publisher | Serbian Society of Mechanics & Mathematical Institute of the Serbian Academy of Sciences and Arts, Belgrade |
| record_format | Article |
| series | Theoretical and Applied Mechanics |
| spelling | doaj.art-6b2d3d6e52274233b1d96f8333c5d6552022-12-22T00:04:43ZengSerbian Society of Mechanics & Mathematical Institute of the Serbian Academy of Sciences and Arts, BelgradeTheoretical and Applied Mechanics1450-55842406-09252021-01-0148220123610.2298/TAM210312009E1450-55842100009ETulczyjew’s triplet for lie groups III: Higher order dynamics and reductions for iterated bundlesEsen Oğul0Gümral Hasan1Sütlü Serkan2Department of Mathematics, Gebze Technical University, Gebze, Kocaeli, TurkeyDepartment of Mathematics, Yeditepe University, Ataşehir, İstanbul, TurkeyDepartment of Mathematics, Işık University, Şile, İstanbul, TurkeyGiven a Lie group 𝐺, we elaborate the dynamics on 𝑇*𝑇*𝐺 and 𝑇*𝑇𝐺, which is given by a Hamiltonian, as well as the dynamics on the Tulczyjew symplectic space 𝑇𝑇*𝐺, which may be defined by a Lagrangian or a Hamiltonian function. As the trivializations we adapted respect the group structures of the iterated bundles, we exploit all possible subgroup reductions (Poisson, symplectic or both) of higher order dynamics.http://www.doiserbia.nb.rs/img/doi/1450-5584/2021/1450-55842100009E.pdfeuler-poincaré equationslie-poisson equationshigher order dynamics on lie groups |
| spellingShingle | Esen Oğul Gümral Hasan Sütlü Serkan Tulczyjew’s triplet for lie groups III: Higher order dynamics and reductions for iterated bundles Theoretical and Applied Mechanics euler-poincaré equations lie-poisson equations higher order dynamics on lie groups |
| title | Tulczyjew’s triplet for lie groups III: Higher order dynamics and reductions for iterated bundles |
| title_full | Tulczyjew’s triplet for lie groups III: Higher order dynamics and reductions for iterated bundles |
| title_fullStr | Tulczyjew’s triplet for lie groups III: Higher order dynamics and reductions for iterated bundles |
| title_full_unstemmed | Tulczyjew’s triplet for lie groups III: Higher order dynamics and reductions for iterated bundles |
| title_short | Tulczyjew’s triplet for lie groups III: Higher order dynamics and reductions for iterated bundles |
| title_sort | tulczyjew s triplet for lie groups iii higher order dynamics and reductions for iterated bundles |
| topic | euler-poincaré equations lie-poisson equations higher order dynamics on lie groups |
| url | http://www.doiserbia.nb.rs/img/doi/1450-5584/2021/1450-55842100009E.pdf |
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