The Interactions of Forces and Motions in a Gyro

Abstract

In the case of gyros that are subject to the action of any kind of forces, we are normally interested in two types of problems: we either have to calculate the forces that are acting when certain types of motions are observed, or we have to determine the motions that occur as the result of the action of known forces. Problems of the first kind can generally be solved without difficulty, because the torques appear in the equations of motion in a linear form. On the other hand, up to the present time it has only been possible to find exact solutions for very few cases of the second type. This is due to the fact that the components of the angular velocity occur in the equations of motion in quadratic form and also as derivatives with respect to time.