Generalized 4th Appelrot class: phase topology

Mech. tverd. tela, 2010, No. 40, pp. 21-33 The article continues the author's publication in [Mech. Tverd. Tela, No. 35, 2005 and No. 38, 2008], in which we investigate the integrable dynamical system induced on one four-dimensional submanifold of the phase space of the problem of a rigid body motion in a double force field. When the intensity of one of the fields tends to zero this systems turns into the family of the espesially remarkable motions of the Kowalevski top belonging to the 4th Appelrot class. We introduce a method to describe the phase topology in the case when algebraic dependency is known of the phase variables in terms of separation variables. This method is based on some construction with Boolean vector functions. For the considered system with two degrees of freedom we fulfil the rough topological analysis.