Analysis of a nutation damper for a two-degree-of-freedom gyroscope

The dynamics of a two-degree-of-freedom gyroscope with a ball-in-tube nutation damper mounted in the gimbal is analyzed. The nonlinear coupled equations of motion are solved by using the method of multiple scales. The results show that, if the natural frequency of the ball-in-tube damper is tuned to equal the nutation frequency of the gyroscope with the damper removed, the wobble motion of the gyroscope will be eliminated most rapidly and the decay time constant of the nutation angle is a concave function of the damping coefficient. If the nutation damper is oriented perpendicular to the spin axis of the rotor, the residual precession due to the gravity effect can be avoided. (Author)