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

Abstract

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