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.