Van der Pol’s Method: A Simple and Classic Solution

Abstract

As early as the year 1920, Van der Pol (1920) Van der Pol (1889–1959) worked on the free and forced oscillations forced oscillations of a triode triode. In the first case, he tackled the determination of an approximate value of the amplitude and period problem, by using the Poincare-Lindstedt method and harmonic analysis. In the paragraph entitled “First Method for finding the Amplitude of the Fundamental”, Van der Pol (1920, 704) recalls that he followed a solving method suggested by Professor Hendrik Antoon Lorentz (1853–1928). It was actually a “variation” of the Poincare-Lindstedt method that Rocard (1932) Rocard (1903–1992) incidentally used a few years later, but which cannot pass the obstacle linked to the presence of secular terms, which “disturb the periodic character of the solution”, as noted by Van der Pol (1920, 706) in a footnote. He thus obtains the value a0 of the amplitude of the fundamental, presented in Table 9.2 above. In the next paragraph, he uses the harmonic analysis and finds the same result.