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

TL;DR

This paper analyzes the bifurcation diagrams of a symmetric top under Kowalevski conditions in a double force field, providing explicit inequalities for critical motions and constructing stable iso-energy level diagrams.

Contribution

It introduces explicit inequalities for the existence of critical motions and constructs all stable bifurcation diagrams on iso-energy levels for the system.

Findings

Derived explicit conditions for critical motions.

Constructed all stable bifurcation diagrams.

Analyzed the system's bifurcation structure in detail.

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.