New Cases of Integrable Ninth-Order Conservative and Dissipative Dynamical Systems

Abstract

New cases of integrable ninth-order dynamical systems that are homogeneous in terms of some of their variables are presented, in which a system on the tangent bundle of a four-dimensional manifold can be distinguished. In this case, the force field is divided into an internal (conservative) and an external one, which has dissipation of different signs. The external field is introduced using some unimodular transformation, and it generalizes previously considered fields. Complete sets of both first integrals and invariant differential forms are given.