ABSTRACT
The stability problem of classical mechanics, that is, the question as to the stability of the solar system, has the fascinated astronomers and the mathematicians for the centuries. With relatively small forces which are carried out periodically at the frequency of the swing one can increase the amplitude of the swing as high as one wants and can even cause the swing to overturn. In the case of the solar system, the simplest resonance phenomena also play a major role. In reality, however, one must expect such resonances for all rational frequency ratios and even those in which a linear combination of the frequencies with the integer coefficients vanishes (commensurable frequencies). This is naturally utterly absurd, for in fact the rational numbers are dense, and from a physical point of the view one cannot distinguish between the rational and irrational frequencies.
