Generalized 4-th Appelrot class: phase topology

The article continues the author's publications (Mekhanika Tverdogo Tela, No 35, 2005 and No 38, 2008) dealing with the investigation of the integrable dynamical system on the four-dimensional invariant subset of the phase space of the problem of motion of a rigid body in a double force field. As one of the fields tends to zero this system turns into the set of especially remarkable motions of the 4-th class of Appelrot in the classical Kowalevski problem. We suggest a method of the phase topology description for the case of algebraic dependencies of the phase variables on the separated variables. This method is based on the use of Boolean vector-functions. The rough topological analysis of the system considered is fulfilled.