Study on the mechanics property of three degrees of freedom air-bearing testbed-influence on the moment of inertia matrix and on the direction of inertia principal axis when acted on gravity

Influences on the moment of inertia matrix and on the direction of inertia principal axis of the platform of air-bearing testbed by the deforming of the platform when acted on gravity are analyzed according to the theory on high kinetics. The principal inertia and inertia product of the platform in various angles are calculated by finite element method. The formulary for the moment of inertia matrix of the platform in any Eulerian angle when considering the first order deforming effect is presented. The result shows that the deformation of platform makes the change on the direction of inertia principal axes which results in an error on the attitude precision. The error is influenced by the value of inertia product on vertical axis and horizontal axis when the platform is acted on gravity along the horizontal axis in the frame attached to the platform. It will be derived from the calculation that the maximum attitude precision error of the platform is 1.4 × 10^-6 rad, which can satisfy the demand on the attitude precision need by satellites.