We continue our investigation of stability of the linear Hamiltonian system which describes the dynamics in a gyroscopic problem. The system has four degrees of freedom and constant coe_cients depending on three parameters. We study stability of the system in the case of zero eigenvalues. We obtaine inequalities which e_ectively isolate the set of stability in the space of param- eters. An alternative way of isolation of the set of stability with the innor's technic is considered. The generalization of the problem on the case of four parameters is considered as well.

Mathematical problems and theory of numerical methods