Singular lagrangians: some geometric structures along the Legendre map

Abstract

New geometric structures that relate the lagrangian and hamiltonian formalisms defined upon a singular lagrangian are presented. Several vector fields are constructed in velocity space that give new and precise answers to several topics like the projectability of a vector field to a hamiltonian vector field, the computation of the kernel of the presymplectic form of lagrangian formalism, the construction of the lagrangian dynamical vector fields, and the characterisation of dynamical symmetries.

27 pages; minor changes, a reference updated

References in corpus (3)

• Anharmonic oscillators, the thermodynamic Bethe ansatz, and nonlinear integral equations
• Fibre derivatives: some applications to singular lagrangians
• Canonical Noether symmetries and commutativity properties for gauge systems

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