Cross-coupling errors of micromachined gyroscopes

A model is developed for the response of a micromachined, rotary gyroscope subject to a general input motion. The governing equations are formulated for weakly nonlinear oscillations of the rotor, suspended above the moving substrate via elastic beams. The method of multiple scales is used to separate the slow and fast responses. This approach allows quick computation of the long-term behavior of the rotor without the need to integrate over fast oscillations. The power of the model to evince cross-coupling errors is demonstrated through examples.