A Pure Hamiltonian Proof of the Maupertuis Principle

Here is another version of proof of Maupertuis’s principle. This version is pure Hamiltonian and independent of the Lagrangian approach. The proof is based upon the  Hamiltonian version of the Vector Field Straightening Theorem. It seems that such a style of exposition simplifies the understanding of this non-trivial construction.   First, recall and briefly discuss...