On an evolution operator connecting Lagrangian and Hamiltonian formalisms (Q581896)

From the Conclusion: ``The intrinsic definition of the evolution operator K, which connects Lagrangian and Hamiltonian formalism, is given by characterizing it through three clear geometrical properties which involve the consideration of sections of vector bundles over the Legendre transformation. This can be used to write intrinsically the equations of motion for the solution paths, avoiding the use of Lagrangian or Hamiltonian vector fields. As a straightforward corollary, it is easily shown that application of K on Hamiltonian constraints yields Lagrangian constraints. It is conceivable that the present approach will lead to new results on the intrinsic relations between Lagrangian and Hamiltonian formalisms. In particular, a geometric constraint algorithm for Lagrangian formalism, including the second-order condition, can be deviced.''