The Euler-Poinsot top: a non-commutatively integrable system without global action-angle coordinates (Q1366334)

The Euler-Poinsot top, i.e. a torque-free rigid body with a fixed point, is discussed from a novel point of view. The approach is based on the so-called non-commutative integrability, and a global geometric description of the system is given through the Poisson's structure on the base of the fibering into two-dimensional invariant tori. The author explains why this system does not possess global generalized action-angle coordinates.