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 such as the projectability of a vector field to a Hamiltonian vector field, the computation of the kernel of the presymplectic form of a Lagrangian formalism, the construction of the Lagrangian dynamical vector fields and the characterization of dynamical symmetries.