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Euler's dynamic equation is derived in vector-dyadic form for a three-degree-of-freedom gyro configuration. This equation is then simplified by means of two approximations which are compatible with practical gyro design. As angular displacements of the gyro gimbals are assumed to be small, such displacements are represented by vector angles. Spring torques, and torques due to viscous damping are formulated and added to the simplified dynamic equation. The over-all formulation is expressed in the form of a single second-order, linear differential equation of motion.