A derivation of three-dimensional error equations for a locally vertical inertial navigation system based on the three-gimbal and five-gimbal concepts. The error equations are presented for undamped and damped systems. The resulting analytical expressions give the inertial navigators' position and azimuth in terms of the sensing instrument performance. These same equations can be used in analyzing the rotational motion of a gravitationally stabilized satellite. The equations of motion reveal a driving function proportional to the orbit eccentricity.
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