Integrable homogeneous dynamical systems with dissipation on the tangent bundle of a three-dimensional manifold

In many problems of dynamics, the position spaces of systems considered are three-dimensional manifolds and hence the phase spaces of such systems are the corresponding tangent bundles. In this paper possess, we consider dynamical systems with variable (alternating) dissipation. We prove the integrability of general classes of homogeneous dynamical systems with variable dissipation on the tangent bundles of three-dimensional manifolds.