Two-Degree-of-Freedom Gyroscopes

Abstract

Following accepted terminology, a gyroscope is essentially a spinning wheel, suspended generally upon bearings and having at least a partial freedom to carry out a change of orientation of its spin axis. We also know that this angular rate of change is proportional to the component of the torque applied perpendicularly to the spin axis. Expressed in this way, the behavior of any gyro is fully explainable by the laws of classical mechanics without any additional assumption. Particularly, Newton’s law of inertia, which relates the time history of the angular momentum vector to a torque input, is directly applicable to any gyroscope. From this point of view, one may say that the whole history of gyro development is dominated by the endeavor of creating and maintaining in a rotating wheel an adequate angular momentum and trying to minimize spurious torque inputs to achieve optimum operational performance. This presentation, oversimplified as it may appear, is truthful enough, considering the hard (and still unfinished) work accumulated since 1852, when Leon Foucault appears to have demonstrated by gyroscopic means (in addition to his famous pendulum) that the earth is rotating about its axis and that this rotation can be utilized to make a gyroscope with a horizontally constrained spin axis seek out the local meridian of the earth.