Generalized 4th Appelrot class: region of existence of motions and separation of variables

We consider the analogue of the 4th Appelrot class of the Kowalevskaya top for the case of double force field. The trajectories of this family fill the 4-dimensional surface in the 6-dimensional phase space. We point out two almost everywhere independent partial integrals that give the regular parametrization of the corresponding sheet of the bifurcation diagram in the complete problem. Projections of the Liouville tori onto the plane of auxiliary variables are investigated. The bifurcation diagram of the partial integrals is found. The region of existence of motions in terms of the integral constants is established. We introduce the change of variables that separate the system of differential equations for this case.