2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/56364We show that the motion on the n-dimensional ellipsoid is complete integrable by exhibiting n integrals in involution. The system is separable at classical and quantum level, the separation of classical variables being realized by the inverse of the momentum map. This system is a generic one in a new class of n-dimensional complete integrable Hamiltonians defined by an arbitrary function f(q,p) invertible with respect to momentum p and rational in the coordinate q.Latex, 8 pages, no figuresHigh Energy Physics - Theorytext