Analytical classification of the permanent rotations of the Kowalevski-Yehia gyrostat

The complete investigation of the permanent rotations of a gyrostat in the integrable case of Kowalevski-Yehia is presented. The notion of equivalence classes is given with respect to the defining parameters, the separating set is constructed. For each class the type of a singularity is calculated as the type of a fixed point in the reduced system. The detailed character of stability is obtained, and the structure of local Liouville foliation is shown.