Dynamics of a Gyroscope With Two Degrees of Freedom

Abstract

Gyroscopes with two degrees of freedom are used to measure the absolute angular velocity of various bodies (aircraft, etc.) (1, 2). The static theory of a two-degree gyroscope starts with the assumption tha t at each instant of t ime the deviation of the gimbal from its reference position in the body is determined by its relative equilibrium under the action of the gyroscopic moment and the moment of the restoring force. This assumption is admissible to a certain extent if the instrument is used only to stabilize the angular position of the object in space or when the disturbing forces on the object are relatively weak. However, when controlling unsteady angular motions of an object or in the case of large disturbances, an estimate of the angular velocity of the object based on static theory may lead to noticeable errors and to the occurrence of false signals. In addition, deviations of the geometric and mass parameters of the instrument from their ideal (rated) values, as occur in actual constructions, impose supplementary errors on the results of the measurement of the angular velocity of the object. I t is therefore advisable to investigate the conditions under which false signals arise in the instrument under arbitrary linear and angular displacements of the object, with allowance for the most substantia] deviations of the actual construction of the instrument from the design data.