Qualitative analysis of the phase flow of a Manev system in a rotating reference frame

The rotating two-body Manev problem is defined by means of the Hamiltonian function with (α, β)∈ℝ+×ℝ being two structural parameters. Using the Liouville–Arnold theorem and a particular analysis of the momentum map in its critical points, we obtain a complete topological classification of the different invariant sets of the phase flow of this problem. This analysis, in some aspects very computational, is made with the help of a standard commercial mathematical package.