Sur Une Des Liaisons Des Equations D’euler Lagrange A Celles De Hamilton Par Le Théorème De L. Noether

Abstract

In this paper, we have traced some theories in physics which are described by the Lagrangian, by the associated Hamiltonian. Then, we made the connection between the Euler-Lagrange equations to those of Hamilton basing on a result we got : « the functions and are reciprocal diffeomorphisms », L represents the Lagrangian of a phenomen. On his the associated Hamiltonian and respectively the generalized coordinate of phenomenon and the conjugate momentum of the Lagrangian with respect to By proving that , which is a solution of the Euler-Lagrange equation, is also a solution of Hamilton equations therefore a first integral. We have joined Noether’s theorem which states that is a first integral where W is an infinitesimal symmetry of the Lagrangian.