ON THE STABILITY OF GYROSCOPIC SYSTEMS

Gyroscopic systems considered here have the form Ay + G(y) over dot Ky = 0 where A, G, K are real n x n matrices with A > 0, G(T) = -G, K- T = K, and the stiffness matrix K has some negative eigenvalues; i.e., the equilibrium position is unstable (when G = 0). A new necessary co ndition for stability is established. It is also shown that gyroscopic systems with K < 0 and G singular are always unstable for G sufficien tly large.