Integration of the Euler-Poinsot Problem in New Variables

TL;DR

This paper introduces a new set of canonical variables for the Euler-Poinsot problem that offers explicit transformation formulas, facilitating the analysis of perturbed rigid-body motion with advantages over traditional action-angle variables.

Contribution

The paper presents an alternative set of variables for the Euler-Poinsot problem with explicit transformation formulas, enhancing analytical convenience over existing methods.

Findings

New variables enable explicit transformations from Andoyer variables.

They perform similarly to action-angle variables in perturbed problems.

Transformations are given in closed-form expressions.

Abstract

The essentially unique reduction of the Euler-Poinsot problem may be performed in different sets of variables. Action-angle variables are usually preferred because of their suitability for approaching perturbed rigid-body motion. But they are just one among the variety of sets of canonical coordinates that integrate the problem. We present an alternate set of variables that, while allowing for similar performances than action-angles in the study of perturbed problems, show an important advantage over them: Their transformation from and to Andoyer variables is given in explicit form.