Bifurcation diagrams on iso-energetic levels of the Kowalevski-Yehia gyrostat

TL;DR

This paper analyzes bifurcation diagrams of the Kowalevski-Yehia gyrostat, establishing explicit motion conditions and creating an electronic atlas of iso-energetic diagrams for better understanding of the system's dynamics.

Contribution

It provides explicit inequalities for motion conditions and constructs a separating set, forming an electronic atlas of bifurcation diagrams for the gyrostat.

Findings

Explicit inequalities for motion conditions derived

Separating set in energy-gyrostatic momentum plane constructed

Electronic atlas of iso-energetic diagrams created

Abstract

We consider the problem of motion of the heavy gyrostat in the case of Kowalevski-Yehia. To classify the bifurcation diagrams on iso-energetic levels we establish the existence of motion conditions in terms of parameters on the bifurcation surfaces. Obtaining these conditions in the form of explicit inequalities we build the separating set in the "energy-gyrostatic momentum" plane. Thus the electronic atlas of iso-energetic diagrams is created.