Integrable homogeneous dynamical systems with dissipation on the tangent bundles of smooth finite-dimensional manifolds. II. Equations of motion on the tangent bundle of an $n$-dimensional manifold in a potential force field

This paper is the second part of the work on the integrability of general classes of homogeneous dynamical systems with variable dissipation on the tangent bundles of $n$-dimensional manifolds. The first part of the paper is: Integrable homogeneous dynamical systems with dissipation on the tangent bundles of smooth finite-dimensional manifolds. I. Equations of geodesics on the tangent bundle of a smooth $n$-dimensional manifold// Itogi Nauki Tekhn. Sovr. Mat. Prilozh. Temat. Obzory, 214 (2022), pp. 82–106.