2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/221940In this study, Hamiltonian and Lagrangian theories, which are mathematical models of mechanical systems, are structured on the horizontal and the vertical distributions of tangent and cotangent bundles. In the end, the geometrical and physical results related to Hamiltonian and Lagrangian dynamical systems are concluded.Dynamical Systems53C15, 70H03, 70H05; PACS: 02.40text