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We establish an implicit variational principle for the equations of thecontact flow generated by the Hamiltonian $H(x,u,p)$ with respect to thecontact 1-form $\alpha=du-pdx$ under Tonelli and Osgood growth assumptions. Itis the first step to generalize Mather's global variational method from theHamiltonian dynamics to the contact Hamiltonian dynamics.

Variational principle for contact Tonelli Hamiltonian systems