Ermakov-Pinney equation for time-varying mass systems

Abstract

We extend Fring-Tenney approach of constructing invariants of constant mass time-dependent system to the case of a time-dependent mass particle. From a coupled set of equations described in terms of guiding parameter functions, we track down a modified Ermakov-Pinney equation involving a time-dependent mass function. As a concrete example we focus on an exponential choice of the mass function.