THE EFFECT OF DAMPING ON THE STABILITY OF GYROSCOPIC PENDULUMS

The paradoxical effects of damping on dynamic stability are reviewed before turning to a detailed analysis of statically stable and statically unstable gyroscopic pendulums. The Thomson and Tait theorem which predicts that a damped statically unstable gyropendulum is unstable at all spin speeds, even though it is stable at high speeds without damping, is discussed. The theorem applies only when the damping is stationary. Rotating damping is introduced and it is shown that with a combination of stationary and rotating damping it is possible for a gyropendulum to have the same stable speed range with damping as without.