Bifurcation diagram of the generalized 4th Appelrot class

TL;DR

This paper analyzes the bifurcation diagram of the generalized 4th Appelrot class in the Kowalevski top under a double force field, extending previous classifications and identifying the structure of trajectories and integrals.

Contribution

It generalizes the 4th Appelrot class for the Kowalevski top in a double force field and determines its bifurcation diagram and admissible regions.

Findings

Bifurcation diagram of the generalized 4th Appelrot class is established.

The admissible region for the integrals is identified.

Trajectories fill a four-dimensional surface near generic points.

Abstract

The article continues the author's publication in [Mech. Tverd. Tela, No. 34, 2004], in which the generalizations of the Appelrot classes of the Kowalevski top motions are found for the case of the double force field. We consider the analogue of the 4th Appelrot class. The trajectories of this family fill the surface which is four-dimensional in the neighborhood of its generic points. The complete system of two integrals is pointed out. For these integrals the bifurcation diagram is established and the admissible region for the corresponding constants is found.