Forschungsberichte Des Landes Nordrhein- Über Die Periodischen Lösungen Der Van Der Polschen Differentialgleichung X.. + µ(X2 -1) X. + X = 0, Book 1307, (Paperback)

Probably it is not an exaggeration to say that, since the time of GALILEO who introduced the concept of the harmonic oscillator, we were able to actually ob- serve a practically perfect physical image of the latter only when the VAN DER POL oscillator became available relatively a short time ago. In fact, very likely, there exists no better physical image of a simple harmonic motion than that which is produced by modern high quality electron tube oscillators, particulary those whose frequency is stabilized by quartz units. But this almost perfect physical image contains a germ of immense complexity due to the presence of an infinite spectrum of frequencies with which the energy fluctuates between the oscillator and the source of energy. These fluctuations escape our observation, however, if iJ. is very small . . . However, it is precisely this hidden complexity of vanishingly small energy fluctuations which permits obtaining a simple harmonie oscillation in its apparently pure form. N. MINORSKY, Energy Fluctuations 1D a VAN DER POL Oscillator, Journal of the Franklin Intitute 248 (1949). Diese Worte MINORSKYS stellen wir voran, um ein Schlaglicht auf die Bedeutung der v AN DER POLS ehen Differentialgleichung zu werfen. Wir verzichten hier darauf, physikalische und technische Einzelheiten näher auszuführen. Beispiele für V orgänge, die die v AN DER POLsehe Differentialgleichung beschreibt, finden sich in der angegebenen Literatur. Schon die Vielzahl der Vorgänge, die der v AN DER POLS ehen Differentialgleichung gehorchen, rechtfertigt ihr genaues Studium.