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A description of time-dependent Mechanics in terms of Lagrangian submanifoldsof Dirac manifolds (in particular, presymplectic and Poisson manifolds) ispresented. Two new Tulczyjew triples are discussed. The first one is adapted tothe restricted Hamiltonian formalism and the second one is adapted to theextended Hamiltonian formalism.

Time-dependent Mechanics and Lagrangian submanifolds of Dirac manifolds