Stable Member Equations of Motion for a Three-Axis Gyro Stabilized Platform

This paper presents a detailed development of the equations of motion for the stable member of a three-axis platform. Kinematic relations are presented for an x, z, y Euler sequence. This development includes the effects of friction, inertia, and torque motors. A set of six first-order differential equations of state are presented representing the equations of motion of the system members. These equations may be integrated and the resulting Euler angles and rates used to describe the stable member motions. When combined with the servo loops, the motion of the stable member represents the angular motion environment of the stable member mounted instruments.