A precise bound for gyroscopic stabilization

We consider gyroscopic systems Mx(t) + hGx(t) + Kx(t) = 0 where M > 0, G(T) = -G, and K < 0. A is shown how to compute a critical value of parameter ( h) over cap which (in many cases) separates stable and unstable regimes for gyroscopic stabilization. Comparison is made with some known, sufficient c onditions for stability or instability, and a theory is developed (includin g the formulation of a related Lyapunov function) which unifies several ear lier results concerning systems of this kind. Numerical examples are includ ed.