Integration of the Euler-Poinsot Problem in New Variables

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.