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We consider the integrable system with three degrees of freedom for whichSokolov and Tsiganov specified Lax representation. Lax representationgeneralizes L-A pair of the Kowalevski gyrostat in two constant fields, foundby A.G.Reyman and M.A.Semenov-Tian-Shansky. In the paper, we give the explicitformulas for the (independent almost everywhere) additional first integrals Kand G. These integrals are functionally connected with factors of a spectralcurve of L-A pair by Sokolov and Tsiganov. Due to this form of additionalintegrals K and G, without constant gyrostatic moment, we managed to findanalytically two invariant four-dimensional submanifolds on which the induceddynamic system is almost everywhere Hamiltonian system with two degrees offreedom. System of equations that describes one of these invariant submanifoldsis a generalization of invariant relations of an integrable Bogoyavlensky casein dynamics of a rigid body. To describe phase topology of the system as awhole we use the method of critical subsystems. For each subsystem, weconstruct the bifurcation diagrams and specify the bifurcations of Liouvilletori both in subsystems, and in the system as a whole.

Phase topology of one nonclassical integrable problem of dynamics