NON-LINEAR GENERALIZATION OF THE GAUGE AMBIGUITIES OF THE LAGRANGIAN FORMALISM
José F. Cariñena, Manuel F. Rañada · International Journal of Modern Physics A · 1991
A generalization of the gauge equivalence of Lagrangians is developed. In this approach the different Lagrangians determine not only the same set of solutions but also the same energies. Some general properties are studied and then the case of velocity-free forces is considered. In particular we show the non-existence for n=2 (two degrees of freedom) of such equivalent Lagrangians and that when n=3 the only forces admitting such equivalent Lagrangians correspond to those deriving from central potentials.