Self-Excited Oscilations : from Poincar\'e to Andronov

TL;DR

This paper reviews the historical development of the theory of self-excited oscillations, focusing on Poincaré's and Andronov's contributions to understanding stable limit cycles in nonlinear systems.

Contribution

It highlights the historical significance and influence of Poincaré and Andronov's work on the development of nonlinear oscillation theory.

Findings

Poincaré introduced the concept of stable limit cycles in 1908.

Andronov linked self-oscillations to stable limit cycles in 1929.

The paper discusses the reception of these ideas in France.

Abstract

In 1908 Henri Poincar\'e gave a series of 'forgotten lectures' on wireless telegraphy in which he demonstrated the existence of a stable limit cycle in the phase plane. In 1929 Aleksandr Andronov published a short note in the Comptes Rendus in which he stated that there is a correspondence between the periodic solution of self-oscillating systems and the concept of stable limit cycles introduced by Poincar\'e. In this article Jean-Marc Ginoux describes these two major contributions to the development of non-linear oscillation theory and their reception in France.