This paper presents a detailed derivation of the equations of motion for the stable member of a four-axis platform. Angular velocity and angular acceleration of gimbal and platform are presented. In gyro dynamics, equations of motion for gyro, output equations, gyro reaction torque are proposed. Sequence of platform and gimbal equations are yaw axis, inner roll axis, pitch axis, and outer roll axis in a row. Derived equations of motion are simulated for the verification. Linearized equations of motion with small gimbal angle are presented. These are necessary for the design of stabilized loop.