Abstract

TORRES DEL CASTILLO, G.F.. Point symmetries of the Euler-Lagrange equations. Rev. mex. fis. [online]. 2014, vol.60, n.2, pp.129-135. ISSN 0035-001X.

We give an elementary derivation of the equations for the point symmetries of the Euler-Lagrange equations for a Lagrangian of a system with a finite number of degrees of freedom. We show that given a divergence symmetry of a Lagrangian, there exists an equivalent Lagrangian that is strictly invariant under that transformation. The corresponding description in the Hamiltonian formalism is also investigated.

Keywords : Lagrangians; symmetries; equivalent Lagrangians; constants of motion; Hamiltonian formalism.