On the KAM - Theory Conditions for the Kirchhoff Top

* Partially supported by Grant MM523/95 with Ministry of Science and Technologies.

In this paper the classical Kirchhoff case of motion of a rigid body in an infinite ideal fluid is considered. Then for the corresponding Hamiltonian system on the zero integral level, the KAM theory conditions are checked. In contrast to the known similar results, there exists a curve in the bifurcation diagram along which the Kolmogorov’s condition vanishes for certain values of the parameters.