The Dynamics of an Imperfect, Multigimbal, Hooke's-Joint Gyroscope

The paper examines the effect of damping and mistuning on the performance of a dynamically-tuned, multigimbal, Hooke's-joint gyroscope. The dynamic stability of the gyro is considered and rotor damping is shown to be a source of instability at rotor speeds in excess of the tuning speed. Using an approximate solution to the governing equations of motion, it is shown that the instrument's capacity to measure either rate of turn or total angular displacement is limited by the degree of mistuning and the damping conditions. The response of the tuned instrument to harmonic inputs at twice rotor frequency is examined and the conditions for a 2ω drift-free gyro are derived.