Systems with dissipation with a finite number of degrees of freedom: analysis and integrability. II. General class of dynamical systems on the tangent bundle of a multidimensional sphere

This paper is the second part of a survey on the integrability of systems with a large number $n$ of degrees of freedom (the first part: Itogi Nauki Tekhn. Sovr. Mat. Prilozh. Temat. Obzory, 211 (2022), pp. 41–74). The review consists of three parts. In the first part, the primordial problem from the dynamics of a multidimensional rigid body placed in a nonconservative force field is described in detail. In this second part, we consider more general dynamical systems on the tangent bundles to the $n$-dimensional sphere. In the third part, which will be published in the next issue, we will consider dynamical systems on the tangent bundles to 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.