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This article is cited in 2 scientific papers (total in 2 papers)
Tulczyjew's triplet for Lie groups III: Higher order dynamics and reductions for iterated bundles
Oğul Esena, Hasan Gümralb, Serkan Sütlüc a Department of Mathematics, Gebze Technical University, Gebze, Kocaeli, Turkey
b Department of Mathematics, Yeditepe University, Ataşehir, İstanbul, Turkey
c Department of Mathematics, Işık University, Şile, İstanbul, Turkey
Abstract:
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.
Keywords:
Euler-Poincaré, equations, Lie-Poisson equations, higher order dynamics on Lie groups.
Received: 12.03.2021 Accepted: 15.06.2021
Citation:
Oğul Esen, Hasan Gümral, Serkan Sütlü, “Tulczyjew's triplet for Lie groups III: Higher order dynamics and reductions for iterated bundles”, Theor. Appl. Mech., 48:2 (2021), 201–236
Linking options:
https://www.mathnet.ru/eng/tam96 https://www.mathnet.ru/eng/tam/v48/i2/p201
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Abstract page: | 60 | Full-text PDF : | 28 | References: | 18 |
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