Response of a Gyropendulum Subject to Parametric Excitation

This paper concerns the response of a gyropendulum subject to vertical harmonic excitation. Instability of the Mathieu type is shown to occur, the principal region of instability lying about the nutational frequency of the system. Experimental results are presented which clearly indicate the validity of the theoretical prediction. It is also shown that an unstable gyroscopic system can be stabilized by vibrating the equipment with the proper choice of vibration parameters. In such cases, the additional stabilizing factor has been analytically derived. Based on the above analysis, practical suggestions for instrument design are also provided.

Dynamics of Gyropendulum for Small Angles

It was shown in (1)‡ that at a given angle of inclination, the gyropendulum may perform steady precession Ω1 or Ω2 and any small disturbance will result in the subsequent motion consisting of precession and nutation, the corresponding nutational frequency being Ω1 or Ω2 respectively. For small angles, Ω1 and Ω2 represent the natural frequencies of the system.