An inverse problem in Lagrangian dynamics based on the preservation of symmetry groups: application to systems with a position-dependent mass

Abstract

An inverse problem in dynamics is proposed, based on a recently formulated symmetry-preserving perturbation method for Lagrangian systems. Special types of systems obtained from kinetic Lagrangians and with a position-dependent mass in two and three dimensions are analyzed in this context, leading in particular to a position-dependent mass version of the generalized Ermakov–Ray–Reid systems. The existence of perturbations modifying the Riemann curvature tensor of the underlying configuration space is shown. As an application, a minimally superintegrable system in three dimensions obtained as perturbation of the position-dependent mass generalization of the Kepler system is constructed.