Zur Theorie der erzwungenen Schwingungen des symmetrischen Kreisels

Summary The object of this paper is to give a theory of the experiments described in the foregoing paper. The applied system of non-linear differential equations byA. Föppl is first solved approximately for small angles, that means small deviations of the axis of the gyroscope from the verticaldirection, the cases without and with consideration of damping force being discussed separately. All characteristic features of the motion observed in the experiments are explained.—After that, an exact particular solution is given for the case of a circular periodic force. An approximate calculation is carried out for the case of a periodic elliptical force acting on afast rotating gyroscope. The solution contains an infinite number of resonance frequencies (subharmonic resonances and resonances with sums and differences of the forced and natural frequencies).