Motion of a three-degree-of-freedom gyro with an electric spring and with zero angular momentum

We consider the motion of a three-degree-of-freedom gyro with an electric spring and with zero angular momentum mounted on a fixed base. The gimbal rotation angles are constrained by an elastic ring that is attached to the base and confines a rod attached to the internal gimbal. The equations of motion of the gyro are supplemented with equations allowing for the delay in the response of the gyro feedback circuit. By numerical integration we find a steady-state mode of the gyro motion, in which the rod alternately slides along the ring and moves in the interior of the ring. This motion can be used to check the gyro performance after launching a spacecraft to a near-Earth orbit by comparing the gyro motions in ground tests and on the orbit.