On the Non-Asymptotic Stability of a Directional Gyroscope

This article examines the behavior of gyroscopic orientation systems, which, unlike inertial navigation systems and gyrocompasses (with internal and external correction), are described solely by Euler's equations. It is shown that, contrary to established views, obtaining the position of the meridian line using a balanced directional gyroscope corrected by information on the transport angular velocity (or a two-axis inertial platform controlled by integrating gyroscopes) is non-asymptotically stable over a wide range of initial conditions, disturbance torques, and parameters of the object's motion on the Earth's surface-more than sufficient for practical use. A comparison of a directional gyroscope and a gyrocompass provides a new interpretation of the role of pendulosity in the design of gyroscopic orientation systems. The fundamental theoretical propositions of the present work are accompanied, to the required extent, by the results of numerical solutions of the equations of motion.