Reduction of Lagrangian mechanics on Lie algebroids |
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| Authors: | José F. Cariñ ena,Joana M. Nunes da Costa,Patrí cia Santos |
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| Affiliation: | 1. Departamento de Física Teórica, Universidad de Zaragoza, 50009 Zaragoza, Spain;2. Departamento de Matemática, Universidade de Coimbra, 3001-454 Coimbra, Portugal;3. Departamento de Física e Matemática, Instituto Superior de Engenharia de Coimbra, 3030-199 Coimbra, Portugal |
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| Abstract: | We prove that if a surjective submersion which is a homomorphism of Lie algebroids is given, then there exists another homomorphism between the corresponding prolonged Lie algebroids and a relation between the dynamics on these Lie algebroid prolongations is established. We also propose a geometric reduction method for dynamics on Lie algebroids defined by a Lagrangian and the method is applied to regular Lagrangian systems with nonholonomic constraints. |
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| Keywords: | 37J15 37J60 70H33 53D |
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