2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/80527We study the separability of the Neumann-Rosochatius system on the n-dimensional sphere using the geometry of bi-Hamiltonian manifolds. Its well-known separation variables are recovered by means of a separability condition relating the Hamiltonian with a suitable (1,1) tensor field on the sphere. This also allows us to iteratively construct the integrals of motion of the system.LaTeX file, 14 pagesExactly Solvable and Integrable SystemsDifferential Geometrytext