ALTERNATIVE LAGRANGIANS FOR CENTRAL POTENTIALS

Two methods for the construction of alternative Lagrangians to the standard Lagrangian L = T - V where V is a central potential are presented: the direct integration of the Hessian matrix and the use of the Noether symmetries of L. The Lagrangians obtained are of the so-called nonlinear homogenous (NLH) type and the study is centered in those Lagrangians not preserving the spherical symmetry of L. Finally, the associated Hamiltonian formalism is presented.