2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/152192Poisson plane and sphere --- homogeneous spaces of Poisson groups E(2) and SU(2) (resp.) --- have phase spaces (corresponding symplectic groupoids), in which a free Hamiltonian is naturally defined. We solve the equations of motion and point out some unexpected features: free motion on the plane is bounded (periodic) and free trajectories on the sphere are all circles except the big ones.LaTeX, 9 pagesDifferential Geometry58F05 (Primary) 22A22, 58H05, 53Z05 (Secondary)text