The universal Lagrangian for one particle in a potential
American Journal of Physics
In a system consisting of a single particle in a potential, the classical ?L dt is the number of phase waves that pass through the moving particle, as the particle moves from its initial to its final position. Thus the Lagrangian can be cast into the form L=p(vg-vp), where vg and vp are the group and phase velocities and p is the momentum.
Evans, James C.. 2003. "The universal Lagrangian for one particle in a potential." American Journal Of Physics 71(5): 457-461.