Tulczyjew's Triplet With an Ehresmann Connection I: Trivialization and Reduction
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Date
2023
Authors
Esen, Ogul
Kudeyt, Mahmut
Sutlu, Serkan
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Publisher
World Scientific Publ Co Pte Ltd
Open Access Color
Green Open Access
Yes
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No
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Abstract
We study the trivialization and the reduction of Tulczyjew's triplet, in the presence of a symmetry and an Ehresmann connection associated to it. We thus establish a geometric pathway for the Legendre transformations on singular dynamical systems.
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Keywords
Lagrangian Submanifolds, Hamiltonian-Structure, Lie, Dynamics, Lagrangian Submanifolds, Geometry, Hamiltonian-Structure, Lie, Poisson, Dynamics, Formalisms, Geometry, Poisson, Mechanics, Formalisms, Systems, Mechanics, Tulczyjew's triplet, Systems, Hamiltonian reduction, Lifts, Lagrangian reduction, Lifts, Ehresmann connection, Lagrangian Submanifolds, Mathematics - Differential Geometry, Hamiltonian reduction, Geometry, FOS: Physical sciences, Mechanics, Hamiltonian-Structure, FOS: Mathematics, 70H33, 70G45, Lie, Formalisms, Mathematical Physics, Hamiltonian-structure, Tulczyjew's triplet, Systems, Mathematical Physics (math-ph), Poisson, Lagrangian submanifolds, Dynamics, Ehresmann connection, Lifts, Differential Geometry (math.DG), Lagrangian reduction
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Fields of Science
01 natural sciences, 0103 physical sciences, 0101 mathematics
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Source
International Journal of Geometric Methods in Modern Physics
Volume
20
Issue
4
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