Hamilton-Jacobi theory for one dimensional autonomous systems using parametric transformations
arXiv:math-ph/0501061
Abstract
A 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 Physics