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.