Dynamic Analysis of a Gyrocompass

After giving the mathematical relation of the offset angle connection between the inner ring and the ballistic, and the mathematical model of the follow-up subsystem, the exact governing equations of gyrocompass with ballistic are given by Lagrange's equations. The explanation of the asymptotical stability about the system equilibrium by Arnold (1961) is shown to be wrong. Then use Liapunov theorem and Mukherjee-Chen theorem (1993) of direct method, Routh-Hurwitz criterion and multiple scales method are applied to study the stability about the equilibrium of the system in some cases.