Analysis of an Offset Unsymmetric Gyroscope With Oblique Rotor Using (3×3) Matrices With Dual-Number Elements

Abstract

Using 3 × 3 matrices of dual-number elements, dynamic equations are obtained for an offset unsymmetric gyroscope with obliquely placed rotor, a generalized six-degree-of-freedom gyroscopic system (shown schematically in Fig. 3). Equations of motion for a special case of the system, a two-frame symmetric gyroscope, conventional in all aspects except the rotor is inclined relative to its spin axis, are deduced; these equations are applied to the study of the effects of a slightly inclined rotor on (a) a two-frame symmetric gyroscope in steady precession and (b) a Faucualt’s gyrocompass.