Dynamics of Vibratory Microgyroscopes. *

In this report we provide a vectorial derivation of the equations of motion characterizing the dynamic behavior of both ideal and non-ideal (e.g., including anisoelastic effects) vibratory micromachined gyroscopes. The derivation pre-sented here utilizes the basis-free Newton-Euler approach (viz., the balance of angular momentum) rather than an energy based formulation. Our approach offers the following advantages: (1) It leads to an explicit set of dynamic equa-tions without requiring excessive symbolic manipulations by the analyst, (2) The resulting nonlinear dynamic model can be readily linearized for use in con-troller/estimator design, (3) Our derivation provides maximal physical insight into the dynamic be vior of micromachined rate sensors, (4) The Newton-Euler approach ca can e readily extended to model multibody effects such as ior of angularly vibrating microgyros in this report our formulation is equally valid for linearly vibrating microgyros. rotor/housing dynamic & coupling. Although we emphasize the dynamic behav-