Sets of stability of multiparameter Hamiltonian systems

We consider a real linear Hamiltonian system with constant coefficients depending on real parameters. We state the necessary and sufficient conditions for stability of the stationary solution of this system at the certain parameter point. The method for computing the set of all the parameter points, at which the stationary solution is stable (i.e. the set of stability), is proposed. The application of the method is demonstrated on a gyroscope problem with four degrees of freedom and with three parameters. Computer algebra, in particularly, the Gröobner basis is used in computations.