Classical ladder functions for Rosen–Morse and curved Kepler–Coulomb systems

Ladder functions in classical mechanics are defined in a similar way as ladder operators in the context of quantum mechanics. In the present paper, we develop a new method for obtaining ladder functions of one dimensional systems by means of a product of two ‘factor functions’. We apply this method to the curved Kepler–Coulomb and Rosen–Morse II systems whose ladder functions were not found yet. The ladder functions here obtained are applied to get the motion of the systems.