2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/122695We study reductions of the Hamiltonian flows restricted to their invariant submanifolds. As examples, we consider partial Lagrange-Routh reductions of the natural mechanical systems such as geodesic flows on compact Lie groups and $n$-dimensional variants of the classical Hess-Appel'rot case of a heavy rigid body motion about a fixed point.20 pagesMathematical PhysicsSymplectic GeometryExactly Solvable and Integrable Systems37J35, 37J15, 53D20text