Variations on the adiabatic invariance: the Lorentz pendulum

TL;DR

This paper investigates a modified Lorentz pendulum with exponentially varying length, revealing significant differences in adiabatic invariance compared to the standard uniform variation case.

Contribution

It introduces a new variant of the Lorentz pendulum with exponential length variation and analyzes its distinct adiabatic behavior.

Findings

Exponential length variation leads to different adiabatic invariance conditions.

Quantitative criteria for adiabatic changes are established.

The physical behavior differs substantially from the standard case.

Abstract

We analyze a very simple variant of the Lorentz pendulum, in which the length is varied exponentially, instead of uniformly, as it is assumed in the standard case. We establish quantitative criteria for the condition of adiabatic changes in both pendula and put in evidence their substantially different physical behavior with regard to adiabatic invariance.