An invariant variational principle for Hamiltonian mechanics

@inproceedings{Golovnev2008AnIV,
  title={An invariant variational principle for Hamiltonian mechanics},
  author={Alexey V. Golovnev and Alexander Ushakov},
  year={2008}
}
It is shown that the action for Hamiltonian equations of motion can be presented in invariant symplectic form. The main part of the article is devoted to the analysis of variational principle for systems on non-exact symplectic manifolds.