In some aerospace vehicles, the tracking sensors which act in a tracking loop as stabilizer are mounted on a two degree of freedom gyro. The gyro must align its rotor axis with the line of sight in order to remove tracking errors. The tracking precision and sensitivity are functions of the gyros performance. One of the main factors in reducing the precision and producing instabilities is nutation vibration. This fluctuating motion, which is a dynamical inherent property of the system, is related to the gyro lateral moment of inertia, the length of gyro and its rotating speed. In order to investigate the capabilities of nutation damper and removing the wobble motion of a freely precessing body, this paper analyzes a ring damper partially filled with viscous liquid with taking into account the behavior of the damper and its subsystems. The equations of motion for the dynamical motion of gyro, are obtained using Lagrangian approach, taking into account the friction of dampers and interaction of the liquid with the system equations of motion.