New invariant relations for the generalized two-field gyrostat

In the paper, we consider a completely integrable Hamiltonian system with three degrees of freedom found by V.V. Sokolov and A.V. Tsiganov. This system is known as the generalized two-field gyrostat. For the case of only gyroscopic forces present, we find new invariant four-dimensional submanifolds such that the induced dynamical systems are almost everywhere Hamiltonian with two degrees of freedom.