A "barbell" in a central force field: A case study in symmetry reduction

TL;DR

This paper introduces a novel symmetry reduction method for dynamical systems using polynomial invariants, demonstrated through a mechanical 'barbell' system in a central force field, enabling efficient computations.

Contribution

It presents a new orbit space reduction technique based on localizations of polynomial invariants, improving computational efficiency for symmetric dynamical systems.

Findings

Effective reduction to a low-dimensional variety

Application to a mechanical 'barbell' system

Enhanced computational efficiency

Abstract

We present an application of a recently introduced variant of orbit space reduction for symmetric dynamical systems. This variant works with suitable localizations of the algebra of polynomial invariants of the group actions, and provides reduction to a variety that is embedded in a low-dimensional affine space, which makes efficient computations possible. As an example, we discuss the mechanical system of a "barbell" in a central force field.