Ermakov-Pinney equation for time-varying mass systems

TL;DR

This paper extends the Ermakov-Pinney equation framework to systems with time-varying mass, providing a method to construct invariants and analyzing a specific exponential mass variation example.

Contribution

It introduces a modified Ermakov-Pinney equation for systems with time-dependent mass, expanding the applicability of invariant construction methods.

Findings

Derived a generalized Ermakov-Pinney equation for variable mass systems

Demonstrated the approach with an exponential mass function example

Provided a new tool for analyzing time-dependent mass dynamics

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.