Stability of non-conservative linear discrete gyroscopic systems

A criterion guaranteeing asymptotic stability of non-conservative, linear gyroscopic systems is derived. The criterion applies to linear systems with internal damping, external damping, and circulatory forces as well as systems with negative definite stiffness matrix. A sufficient condition of flutter instability is also presented. The condition is shown applicable to both conservative and non-conservative gyroscopic systems. An application of the stability criteria explains why internal damping destabilizes a rotating system when operated above critical speed. It is also shown that the critical speed of a gyroscopic system is not an absolute stability measure; the critical speed depends on the frame of reference.