The fact that a non-relativistic particle describes an orbit imposes a restriction on the functional form of the Lagrangian. For a classical particle subjected to an arbitrary local ‘generalized force,’ the (local) Lagrangian is shown to involve, at highest, first, second and third time-derivatives of the position respectively, in one, two and three dimensions. The generalization in the quantum regime is indicated with the aid of Feynman's path integrals.