Time-dependent Mechanics and Lagrangian submanifolds of Dirac manifolds
E. Guzm\'an, J.C. Marrero
TL;DR
This paper presents a geometric framework for time-dependent mechanics using Lagrangian submanifolds of Dirac manifolds, introducing two new Tulczyjew triples for different Hamiltonian formalisms.
Contribution
It introduces a novel geometric approach to time-dependent mechanics via Lagrangian submanifolds of Dirac manifolds and develops two new Tulczyjew triples for Hamiltonian formalisms.
Findings
Two new Tulczyjew triples are constructed.
A geometric description of time-dependent mechanics is provided.
Framework unifies presymplectic and Poisson structures.
Abstract
A description of time-dependent Mechanics in terms of Lagrangian submanifolds of Dirac manifolds (in particular, presymplectic and Poisson manifolds) is presented. Two new Tulczyjew triples are discussed. The first one is adapted to the restricted Hamiltonian formalism and the second one is adapted to the extended Hamiltonian formalism.
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