  The general integrability cases in the rigid-body dynamics are the solutions
of Lagrange, Euler, Kovalevskaya, and Goryachev-Chaplygin. The first two can be
included in Smale's scheme for studying the phase topology of natural systems
with symmetries. We modify Smale's program to suit the most complicated last
two cases with non-linear first integrals. The bifurcation sets are found and
all transformations of the integral tori are described and classified. New
non-trivial bifurcation of a torus is established in the Kovalevskaya and
Goraychev-Chaplygin cases.
