Geodesic and Newtonian Vector Fields and Symmetries of Mechanical Systems

Geodesic vector fields and other distinguished on a Riemann manifold were used in the study of free motions such manifold, we applied geometric Hamilton–Jacobi theory for search geodesic from same closed fields. These properties appropriately extended to framework Newtonian generalised systems, particular systems defined by Lagrangians mechanical type velocity-dependent forces. Conserved quantities concept symmetry developed, particularly Killing Nonholonomic constrained also analysed this perspective, as well relation among equations conformally related metrics.