Smooth trajectories on toroidal manifolds

Abstract

In the recent paper trajectories of the natural motion on toroidal manifolds are considered. It is represented an information dealing with description of the rotation metric at the different methods of toroidal analytical fixing, description of geodesic integrals, links between global motion invariants of the trajectory with the toroidal manifolds parameters. Analytical representations of geodesics at the different values of the global invariants are given.