Regions of existence of critical motions for the generalized Kowalevski top and bifurcation diagrams

Abstract

The paper concludes the cycle of investigations on the bifurcation diagrams of the system with three degrees of freedom which describes the motion of an axially symmetric top with the Kowalevski conditions in a double force field. The explicit inequalities are obtained defining the conditions for the existence of the critical motions on the surfaces bearing the bifurcation diagram (see M.P.Kharlamov, Mekh. Tverd. Tela, 2004, No. 34). We fulfill the construction of all diagrams on iso-energy levels having a stable type with respect to the physical parameters and the energy value.