Gyroscope in a Cardan suspension

Abstract

While the Cardan suspension of a gyroscope has been used for about 150 years [F. Bohnenberger (1817), L. Foucault (1852)], its effect on the motion and stability of the gyroscope has been investigated only during the last 25 years. See, for example, E. L. Nikolai [1, 2], H. Poritsky [1], B. T. Plymale and R. Goodstein [1], K. Magnus [1], R. Grammel and H. Ziegler [1], N. G. Cetaev [3], and others. E. L. Nikolai in 1939 investigated the inertial motion of a balanced symmetric gyroscope in a Cardan suspension, taking into account the masses of the gimbals, and the stability of the motion in the case of a large angular velocity. He also investigated the effect of the magnitude and direction of the angular velocity of the outer gimbal on the stability of the axis of the gyroscope in the vertical position and discovered a curious phenomenon. K. Magnus [2] showed that a similar phenomenon also occurs in the case of a non-balanced symmetric gyroscope in a Cardan suspension. In the same paper he obtained by means of a Lyapunov V-function sufficient conditions for the stability of rotation of the gyroscope about the vertical axis of the outer gimbal of a Cardan suspension.