Invariants of Geodesic, Potential, and Dissipative Systems with Three Degrees of Freedom

Tensor invariants (first integrals and differential forms) of homogeneous dynamical systemson the tangent bundles of smooth three-dimensional manifolds (systems with three degrees offreedom) are presented in this paper. The connection between the presence of such invariants andthe complete set of the first integrals needed for the integration of geodesic, potential, anddissipative systems is shown. At the same time, the force fields introduced make the systems inquestion dissipative with dissipation of different signs and generalize the previously consideredones.