2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/57967A necessary and sufficient condition for a parameter transformation that leaves invariant the energy of a one dimensional autonomous system is obtained. Using a parameter transformation the Hamilton-Jacobi equation is solved by a quadrature. An example of this approach is given.Departamento de Matematicas y Fisica (ITESO). Submitted to Annals of PhysicsMathematical Physics45.20.Jjtext