Integrable Ninth-Order Dynamical Systemswith Dissipation

We present new cases of integrable ninth-order dynamical systems that are homogeneous in part of the variables and in which a system on the cotangent bundle of a four-dimensional manifold can be isolated. Here the force field splits into an internal (conservative) field and an external field; the latter may have dissipation of either sign. The external field is introduced with the use of some unimodular transformation and generalizes the earlier-considered fields. Complete sets of first integrals as well as of invariant differential forms are given.