We consider a linear Hamiltonian system with four degrees of freedom and with constant coecients depending on three parameters. The system describes the dynamics in a gyroscopic problem. The set of stability is the set of those values of parameters, for which the stationary point of the initial Hamiltonian system is stable. The set of stability of rather complicated structure is isolated, and it's structure is investigated with the help of elimination theory and computer algebra. The boundary of this set is a part of a ruled surface. The structure of the set of stability is investigated at the singularities and at innity. It turned out that physical values of parameters which belong to the set of stability form two simply connected domains. Earlier, only a small part of one of these domains of stability was known.

Mathematical problems and theory of numerical methods