Singular Lagrangians: some geometric structures along the Legendre map

@article{Grcia2001SingularLS,
  title={Singular Lagrangians: some geometric structures along the Legendre map},
  author={Xavier Gr{\`a}cia and Josep M. Pons},
  journal={Journal of Physics A},
  year={2001},
  volume={34},
  pages={3047-3070}
}
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… 
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