Geometric adiabatic angle in anisotropic oscillators

TL;DR

This paper explores how action variables are not conserved in classical anisotropic oscillators and Foucault pendulums under slow parameter changes, highlighting the role of mass and frequency in time-dependent systems.

Contribution

It provides a detailed analysis of non-conservation of action variables in anisotropic oscillators and pendulums with adiabatic parameter variations, emphasizing the significance of mass and frequency.

Findings

Action variables are not conserved during adiabatic evolution.

Mass parameter plays a crucial role alongside frequency.

Illustrates non-conservation using Foucault pendulum and anisotropic oscillators.

Abstract

We discuss a classical anisotropic oscillator and the Foucault pendulum as examples illustrating non-conservation of action variables in integrable classical mechanical systems with adiabatically slow evolution. We also emphasize the importance of the mass parameter of a harmonic oscillator, alongside its frequency, in explicitly time-dependent situations.