The electronic atlas of bifurcation diagrams of the Kowalevski-Yehia gyrostat

Abstract

The integrable case of Kowalevski-Yehia in the dynamics of a gyrostat is considered. We present the new way to classify the bifurcation diagrams of the reduced systems. We find the efficiently checked existence conditions for the critical motions on the area integral constant sections of the surfaces bearing the 3-diagram of the complete system. The cases when these conditions qualitatively change give the analytical expressions of the dependencies between the area constant and the gyrostatic momentum forming the classifying set for the two-parametric family of the reduced systems diagrams. Finally, we present the computer system, which satisfy the given definition of the electronic atlas.