COMPLETE REDUCTION OF THE EULER-POINSOT PROBLEM

We propose a new way of defining the Serret-Andoyer variables that does not call on spherical trigonometry. We use those variables to present a complete solution of the Euler-Poinsot problem in the phase space determined by the components of the angular momentum along the principal axes of inertia. We use the solution to convert directly the Serret-Andoyer variables into action-and angle variables, thereby making the Hamiltonian dependent on only two momenta.