  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.
