The Motion Due to Slow Precession of a Gyroscope Driven and Supported by a Hooke's Joint

The movements of a special gyroscopic system due to precession are considered. The system consists of a rotor driven through a directionally-free coupling, an arrangement which has found use in certain control instruments. When the system is precessed at uniform velocity about an axis perpendicular to the driving axis, relative angular deflexion of the rotor takes place. In general, the rotor axis follows a spiral path, ultimately attaining an equilibrium position relative to the driving axis. When precession is stopped the rotor axis returns by a separate path to its zero position. These motions depend on the properties of the system, in particular: (1) rotor spin, (2) rotor windage torque, (3) friction at coupling joints, (4) inertia of driving system, (5) precessional velocity, (6) rotor inertia. The paths resulting from changes in each of these variables are studied experimentally, and theoretical methods are developed for predicting the equilibrium positions and form of rotor paths for such a system.