Odd-order integrable dynamical systems with dissipation

In this paper, we prove the integrability of some classes of odd-order dynamical systems (namely, systems of order 3, 5, and 7), which are homogeneous in some variables and contain a system on the tangent bundle of a smooth manifolds. In this case, we separate force fields into internal (conservative) and external, which has sign-alternating dissipation. External fields are introduced by using some unimodular transformations and generalize fields considered earlier.