THE EFFECT OF DAMPING ON THE STABILITY OF GYROSCOPIC PENDULUMS

The paradoxical effects of damping on dynamic stability are reviewed b efore turning to a detailed analysis of statically stable and statical ly unstable gyroscopic pendulums. The Thomson and Tait theorem which p redicts that a damped statically unstable gyropendulum is unstable at all spin speeds, even though it is stable at high speeds without dampi ng, is discussed. The theorem applies only when the damping is station ary. Rotating damping is introduced and it is shown that with a combin ation of stationary and rotating damping it is possible for a gyropend ulum to have the same stable speed range with damping as without.