Systems with four degrees of freedom with dissipation: analysis and integrability

This paper is a survey on integrable systems with four degrees of freedom whose phase spaces are tangent bundles of four-dimensional smooth manifolds. First, we discuss in detail the original problem from the dynamics of a multidimensional rigid body in a nonconservative force field; then we consider general dynamical systems on the tangent bundles of a sufficiently large class of smooth manifolds and prove sufficient conditions for the integrability of the dynamical systems considered in the class of transcendental.