## Posts Tagged ‘**Van der Pol**’

## Van der Pol and the history of relaxation oscillations

Jean-Marc Ginoux, Christophe Letellier

Relaxation oscillations are commonly associated with the name of Balthazar van der Pol via his eponymous paper (Philosophical Magazine, 1926) in which he apparently introduced this terminology to describe the nonlinear oscillations produced by self-sustained oscillating systems such as a triode circuit.

Our aim is to investigate how relaxation oscillations were actually discovered. Browsing the literature from the late 19th century, we identified four self-oscillating systems in which relaxation oscillations have been observed:

i) the series dynamo machine conducted by Gerard-Lescuyer (1880),

ii) the musical arc discovered by Duddell (1901) and investigated by Blondel (1905),

iii) the triode invented by de Forest (1907)

and, iv) the multivibrator elaborated by Abraham and Bloch (1917).

The differential equation describing such a self-oscillating system was proposed by Poincare for the musical arc (1908), by Janet for the series dynamo machine (1919), and by Blondel for the triode (1919). Once Janet (1919) established that these three self-oscillating systems can be described by the same equation, van der Pol proposed (1926) a generic dimensionless equation which captures the relevant dynamical properties shared by these systems. Van der Pol’s contributions during the period of 1926-1930 were investigated to show how, with Le Corbeiller’s help, he popularized the “relaxation oscillations” using the previous experiments as examples and, turned them into a concept….

… Read more at http://arxiv.org/pdf/1408.4890v1.pdf