The Motion of a Gyroscope Mounted in Gimbals

Abstract

Equations of motion of an astatic gyroscope mounted in gimbals in presence of a viscous friction in the gimbals axes have the form [33] $$\left[ {{A_2} + (A + {A_1}){{\cos }^2}\beta + {C_1}} \right]\frac{{{d^2}\alpha }}{{d{T^2}}} + ({C_1} - A - {A_1})\sin (2\beta )\frac{{d\alpha }}{{dT}}\frac{{d\beta }}{{dT}} + H\cos \beta \frac{{d\beta }}{{dT}} + {n_1}\frac{{d\alpha }}{{dT}} = 0$$ (49.1) $$(A + {B_1})\frac{{{d^2}\beta }}{{d{T^2}}} - \frac{1}{2}({C_1} - A - {A_1})\sin (2\beta ){\left( {\frac{{d\alpha }}{{dT}}} \right)^2} - H\cos \beta \frac{{d\alpha }}{{dT}} + {n_2}\frac{{d\beta }}{{dT}} = 0$$ .