Exact dynamical and kinematical equations governing motions of a two-degree-of-freedom gyroscope mounted on a moving vehicle are formulated. From these equations, a set of simpler ones is derived by taking advantage of a number of experimentally verifiable facts, and this set is solved for a vehicle performing oscillations of small amplitude about an axis having an arbitrary orientation. The validity of the resulting drift theory is established by comparing its predictions with those of digital computer solutions of the exact equations of motion, and formulas relating drift rates to system parameters are presented.

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