Systems with dissipation with five degrees of freedom: Analysis and integrability. II. Dynamical systems on tangent bundles

The work contains the second and third parts of the survey on the integrability of systems with five degrees of freedom (the first part: Itogi Nauki Tekhn. Sovr. Mat. Prilozh. Temat. Obzory, 208, (2022), pp. 91–121). In the first part, the primordial problem from the dynamics of a multidimensional rigid body placed in a nonconservative force field was described in detail. In the second and third parts, we consider more general dynamical systems on tangent bundles to the five-dimensional sphere and other smooth manifolds of a sufficiently wide class. Theorems on sufficient conditions for the integrability of the considered dynamical systems in the class of transcendental functions are proved.