THE GYROSCOPIC PENDULUM OR PENDULOUS
§1. General Properties
65. The Gyro-Pendulum. - A gyroscope mounted so that the center of gravity is either below or above the intersection of two horizontal perpendicular axes about which the system can oscillate is called a gyroscopic pendulum, gyro-pendulum, or pendulous gyroscope. Since a gyro-pendulum with the center of mass below the point of support has greater stability than a compound pendulum of equal mass, it is much used for stabilizing cameras, telescopes and other instruments subject to accelerations on ships and airplanes. Some forms of gyro-compasses and ship stabilizers are pendulous gyroscopes. Inverted gyro-pendulums have been used to stabilize vehicles that are statically unstable such as vehicles designed to operate on a single rail. A gyro-pendulum may be arranged to oscillate in one plane like an ordinary pendulum, or may be arranged to oscillate as a conical pendulum.
A gyroscope fastened to an oscillating body so as to apply a periodic torque to the body, may be arranged in such a manner that the successive vibrations of the oscillating body may be either increased or diminished. Such results depend upon the principle proved in Art. 25. In case a periodic torque acts upon an oscillating body of the same frequency, (a) energy will be imparted to the oscillating body at the maximum rate, and the amplitude of vibration will increase at the maximum rate, when the torque is in phase with the angular velocity of the oscillating body; (b) energy will be abstracted from the oscillating body, and the amplitude of vibration will diminish at the maximum rate, when the torque is in opposite phase to the angular velocity of the oscillating body.
66. The Period and the Equivalent Length of a Gyroscopic Conical Pendulum. - In Fig. 85, the center of gravity of the rotating system of weight mg is at a distance 1 from the point of support C. The gravitational torque L is counter-clockwise about a horizontal axis through C perpendicular to the plane of the diagram. The angular momentum about the spin-axle is repre