History of Nonlinear Oscillations Theory in France (1880–1940)

Archimedes 49 New Studies in the History and Philosophy of Science and Technology Jean-Marc Ginoux History of Nonlinear Oscillations Theory in France (1880–1940) History of Nonlinear Oscillations Theory in France (1880–1940) Archimedes NEW STUDIES IN THE HISTORY AND PHILOSOPHY OF SCIENCE AND TECHNOLOGY VOLUME 49 EDITOR JED Z. BUCHWALD, Dreyfuss Professor of History, California Institute of Technology, Pasadena, USA. ASSOCIATE EDITORS FOR MATHEMATICS AND PHYSICAL SCIENCES JEREMY GRAY, The Faculty of Mathematics and Computing, The Open University, UK. TILMAN SAUER, Johannes Gutenberg University Mainz, Germany ASSOCIATE EDITORS FOR BIOLOGICAL SCIENCES SHARON KINGSLAND, Department of History of Science and Technology, Johns Hopkins University, Baltimore, USA. MANFRED LAUBICHLER, Arizona State University, USA ADVISORY BOARD FOR MATHEMATICS, PHYSICAL SCIENCES AND TECHNOLOGY HENK BOS, University of Utrecht, The Netherlands MORDECHAI FEINGOLD, California Institute of Technology, USA ALLAN D. FRANKLIN, University of Colorado at Boulder, USA KOSTAS GAVROGLU, National Technical University of Athens, Greece PAUL HOYNINGEN-HUENE, Leibniz University in Hannover, Germany TREVOR LEVERE, University of Toronto, Canada JESPER LÜTZEN, Copenhagen University, Denmark WILLIAM NEWMAN, Indiana University, Bloomington, USA LAWRENCE PRINCIPE, The Johns Hopkins University, USA JÜRGEN RENN, Max Planck Institute for the History of Science, Germany ALEX ROLAND, Duke University, USA ALAN SHAPIRO, University of Minnesota, USA NOEL SWERDLOW, California Institute of Technology, USA ADVISORY BOARD FOR BIOLOGY MICHAEL DIETRICH, Dartmouth College, USA MICHEL MORANGE, Centre Cavaillès, Ecole Normale Supérieure, France HANS-JÖRG RHEINBERGER, Max Planck Institute for the History of Science, Germany NANCY SIRAISI, Hunter College of the City University of New York, USA Archimedes has three fundamental goals; to further the integration of the histories of science and technology with one another: to investigate the technical, social and practical histories of specific developments in science and technology; and finally, where possible and desirable, to bring the histories of science and technology into closer contact with the philosophy of science. 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More information about this series at http://www.springer.com/series/5644 Jean-Marc Ginoux History of Nonlinear Oscillations Theory in France (1880–1940) 123 Jean-Marc Ginoux Archives Henri Poincaré, CNRS, UMR 7117 Université de Nancy France Laboratoire des Sciences de l’Information et des Systèmes, CNRS, UMR 7296 Université de Toulon La Valette du Var France ISSN 1385-0180 ISSN 2215-0064 (electronic) Archimedes ISBN 978-3-319-55238-5 ISBN 978-3-319-55239-2 (eBook) DOI 10.1007/978-3-319-55239-2 Library of Congress Control Number: 2017937654 © Springer International Publishing AG 2017 This work is subject to copyright. All rights are reserved by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or information storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. The use of general descriptive names, registered names, trademarks, service marks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. The publisher, the authors and the editors are safe to assume that the advice and information in this book are believed to be true and accurate at the date of publication. Neither the publisher nor the authors or the editors give a warranty, express or implied, with respect to the material contained herein or for any errors or omissions that may have been made. The publisher remains neutral with regard to jurisdictional claims in published maps and institutional affiliations. Printed on acid-free paper This Springer imprint is published by Springer Nature The registered company is Springer International Publishing AG The registered company address is: Gewerbestrasse 11, 6330 Cham, Switzerland to Elisa. If we wish to foresee the future of mathematics, our proper course is to study the history and present condition of the science.1 1Henri Poincaré, Science and Method, 1914, p. 25. Foreword I first heard of Jean-Marc Ginoux when he published his discovery of Poincaré’s lectures on oscillations and limit cycles at the School of Posts and Telegraphs in 1908. As he made clear, their significance was considerable. Because they had been omitted from the eleven volumes of Œuvres de Poincare and as a result had been completely forgotten, there was a gap in our understanding of the contributions of the great French mathematician and physicist. What Ginoux went on to investigate was the even greater gap that this pointed to in our understanding of oscillation theory. The household names in the field are those of the Dutchman Van der Pol and the Russian Aleksandr Andronov, who are remembered for their work in the 1920s, Van der Pol for the oscillator that bears his name and Andronov for among other things being apparently the first to connect the work of engineers and technologists with Poincaré’s discoveries in the early 1880s. The first thing that Ginoux’s discoveries made clear was that Poincaré had made this connection himself and had done so in lectures and in print to an audience of appropriate specialists. This was one of a number of contributions that he made to technology at the time, which makes its subsequent disappearance all the more striking. What Ginoux then discovered was that there had been a considerable investiga- tion into oscillation theory by many French investigators, and his account of this work forms the major part of this book. He introduces us to numerous mysterious devices, explains how experiments and theories of them evolved, and isolates their key novel feature, which was known at the time as the relaxation effect. His account sorts out numerous misconceptions and builds up to an important international conference, the Institut Henri Poincaré in 1933, that was dominated by Van der Pol and French and Russian speakers. Paradoxically, the meeting also lapsed from the community’s memory, and Ginoux traces this to the unequal development of the subject in the two countries. The French engineers did not build an adequate theoretical framework with a substantial commitment of people and resources; the Russians did. As a result, he suggests the subjects passed for a time in the Soviet Union, before awakening again the international interest in dynamical systems. ix x Foreword It is evident that Ginoux’s work is both interdisciplinary and international. It has much to say to both mathematicians and engineers; it establishes new features of the context for their work, both the interactions and the failures; it has a French core and a Russian dimension. It is based throughout on rich, often forgotten, archival material, and it establishes the historical record for the first time. Emeritus Professor Jeremy Gray Open University, Leeds, UK Preface In the history of mathematics, from the nineteenth century, the extraordinary growth of the theory of dynamical systems is distinguished by a hitherto unknown development. This history resulted in several publications. The latest is the excellent article “Writing the history of dynamical systems and chaos: long life and revo- lution, disciplines and culture” by D. Aubin and A. Dahan Dalmedico (Historia Mathematica, 29 (2002), 273–339). Before the present general historical survey that offers us Jean-Marc Ginoux, as far as I know, the only book on this subject, written at the specialist level, is that of E.S. Boïko, published under the Russian title Skola Akademika A.A. Andronova (The Academician A.A. Andronov School, Izdatelsvo Nauka, Moscow, 1983). Although the introduction is devoted to important results achieved outside the USSR, among them the first rank key role played by what might be called the French School and its Poincaré leader, Boïko’s book focuses primarily on the work carried on in Gorky (now Nizhny Novgorod), a city forbidden to foreigners at the time of the Soviet Union. Concerning this topic, it should be noted that some 60 years ago, American mathematicians J.P. La Salle and S. Lefschetz already noticed the lead taken by the researches in the USSR, in the framework of the Gorky School (qualitative methods) and the Kiev School (analytical methods), when they wrote: In USSR the study of differential equations has profound roots, and in this subject the USSR occupies incontestably the first place. One may also say that Soviet specialists, far from working in vacuum, are in intimate contact with applied mathematicians and front rank engineers. This has brought great benefits to the USSR and it is safe to say that USSR has no desire to relinquish these advantages.2 About the book History of Nonlinear Oscillations Theory by Jean-Marc Ginoux (Springer-Verlag, 2016), it is important to note that the germ of the theory of nonlinear oscillations, becoming after the theory of dynamical systems, occurred at a time when most mathematicians saw a source of inspiration for mathematical 2J.P. Lasalle and S. Lefschetz, “Recent soviet contributions to ordinary differential equations and nonlinear mechanics,” Journal of Mathematical Analysis and Applications, 2, 1961, pp 467–499.

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