Time-dependent Mechanics and Lagrangian submanifolds of Dirac manifolds

E. Guzmán, J. C. Marrero

Published 2010-09-01, updated 2010-10-21Version 2

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.