History of nonlinear oscillations theory in France (1880-1940)

This book reveals the French scientific contribution to the mathematical theory of nonlinear oscillations and its development. The work offers a critical examination of sources with a focus on the twentieth century, especially the period between the wars. Readers will see that, contrary to what is o...

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Bibliographic Details
Main Author: Ginoux, Jean-Marc, (Author)
Format: eBook
Language: English
Published: Cham, Switzerland : Springer, 2017.
Series: Archimedes (Dordrecht, Netherlands) ; v. 49.
Subjects:
Nonlinear oscillations > History.
elektronické knihy
electronic books
ISBN: 9783319552392
9783319552385
Physical Description: 1 online resource (xxxvii, 381 pages) : illustrations (some color)

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100 1 |a Ginoux, Jean-Marc,  |e author. 
245 1 0 |a History of nonlinear oscillations theory in France (1880-1940) /  |c Jean-Marc Ginoux. 
264 1 |a Cham, Switzerland :  |b Springer,  |c 2017. 
300 |a 1 online resource (xxxvii, 381 pages) :  |b illustrations (some color) 
336 |a text  |b txt  |2 rdacontent 
337 |a počítač  |b c  |2 rdamedia 
338 |a online zdroj  |b cr  |2 rdacarrier 
490 1 |a Archimedes,  |x 1385-0180 ;  |v volume 49 
504 |a Includes bibliographical references and indexes. 
505 0 |a Foreword; Preface; Translator's Preface; Acknowledgments; Contents; List of Figures; List of Tables; Introduction; Part I From Sustained Oscillations to Relaxation Oscillations; 1 From the Series-Dynamo Machine to the Singing Arc: Gérard-Lescuyer, Blondel, Poincaré; 1.1 The Series Dynamo Machine: The Expression of Nonlinearity; 1.1.1 Jean-Marie-Anatole Gérard-Lescuyer's Paradoxical Experiment; 1.1.2 Théodose du Moncel's Electrokinetic Interpretation of the Paradox; 1.1.3 Aimé Witz's Geometrical Interpretationof the Paradox; 1.1.3.1 Principle of Witz's Construction. 
505 8 |a 1.1.4 Paul Janet's Incomplete Equation Modeling (I)1.2 The Singing Arc: Sustained Oscillations; 1.2.1 William Du Bois Duddell's Revision of Thomson's Formula; 1.2.1.1 Conditions for Starting the Oscillations Sustained by the Singing Arc; 1.2.1.2 Frequency of the Oscillations Sustained by the Singing Arc; 1.2.2 Edlund and Luggin's Work On the Concept of ``Negative Resistance''; 1.2.3 André Blondel's Work and the Non-existenceof a c.e.m.f.; 1.3 The ``Arc Hysteresis'' Phenomenon: Hysteresis Cycles or Limit Cycles?; 1.3.1 The Static and Dynamic Characteristics of the Arc. 
505 8 |a 1.3.1.1 Characteristic of the Direct Current Arc1.3.1.2 Dynamic Characteristic of the Alternating Current Arc; 1.3.2 Hertha Ayrton's Works; 1.3.3 André Blondel's Work On the Singing ArcPhenomenon; 1.3.4 Théodore Simon's Work: The Hysteresis Cycle; 1.3.5 Heinrich Barkhausen's Work; 1.3.6 Ernst Ruhmer's Work; 1.4 Henri Poincaré's ``Forgotten'' Lectures: The Limit Cycles in 1908; 1.4.1 Setting into Equation the Oscillations Sustained by the Singing Arc; 1.4.2 The Singing Arc's Electromotive Force; 1.4.3 Stability of the Sustained Oscillations and LimitCycles. 
505 8 |a 1.4.4 ``Poincaré Stability'' and ``Lyapunov Stability''2 The Great War and the First Triode Designs: Abraham, Bloch, Blondel, Van der Pol; 2.1 The Great War and the Rise of Wireless Telegraphy: The T.M. Valve and the Multivibrator; 2.1.1 General Ferrié: From Wireless Telegraphy to the Eiffel Tower; 2.1.2 The T.M. Valve: Télégraphie Militaire; 2.1.3 The Multivibrator: From the Thomson-Type Systems to Relaxation Systems; 2.2 The Three-Electrode Valve or Triode: Sustained Oscillations; 2.2.1 Paul Janet's Work: Analogy and Incomplete Equation Modeling (II). 
505 8 |a 2.2.2 André Blondel: The Anteriority of the Writing of the Triode Equation2.2.2.1 Modeling; 2.2.2.2 Writing the Equation; 2.2.2.3 Calculating the Fundamental's Period and Amplitude; 2.2.2.4 Classifying Oscillations; 2.3 Balthasar Van der Pol's Equation for the Triode; 2.3.1 Modeling; 2.3.2 Writing the Equation; 2.3.3 Calculating the Period and Amplitudeof the Oscillations; 3 Van der Pol's Prototype Equation: Existence and Uniqueness of the Periodic Solution Cartan, Van der Pol, Liénard; 3.1 Janet and Cartan's Work; 3.1.1 Janet's Preface. 
506 |a Plný text je dostupný pouze z IP adres počítačů Univerzity Tomáše Bati ve Zlíně nebo vzdáleným přístupem pro zaměstnance a studenty 
520 |a This book reveals the French scientific contribution to the mathematical theory of nonlinear oscillations and its development. The work offers a critical examination of sources with a focus on the twentieth century, especially the period between the wars. Readers will see that, contrary to what is often written, France's role has been significant. Important contributions were made through both the work of French scholars from within diverse disciplines (mathematicians, physicists, engineers), and through the geographical crossroads that France provided to scientific communication at the time. This study includes an examination of the period before the First World War which is vital to understanding the work of the later period. By examining literature sources such as periodicals on the topic of electricity from that era, the author has unearthed a very important text by Henri Poincaré, dating from 1908. In this work Poincaré applied the concept of limit cycle (which he had introduced in 1882 through his own works) to study the stability of the oscillations of a device for radio engineering. The "discovery" of this text means that the classical perspective of the historiography of this mathematical theory must be modified. Credit was hitherto attributed to the Russian mathematician Andronov, from correspondence dating to 1929. In the newly discovered Poincaré text there appears to be a strong interaction between science and technology or, more precisely, between mathematical analysis and radio engineering. This feature is one of the main components of the process of developing the theory of nonlinear oscillations. Indeed it is a feature of many of the texts referred to in these chapters, as they trace the significant developments to which France contributed. Scholars in the fields of the history of mathematics and the history of science, and anyone with an interest in the philosophical underpinnings of science will find this a particularly engaging account of scientific discovery and scholarly communication from an era full of exciting developments. 
590 |a SpringerLink  |b Springer Complete eBooks 
650 0 |a Nonlinear oscillations  |x History. 
655 7 |a elektronické knihy  |7 fd186907  |2 czenas 
655 9 |a electronic books  |2 eczenas 
776 0 8 |i Print version:  |a Ginoux, Jean-Marc.  |t History of nonlinear oscillations theory in France (1880-1940).  |d Cham, Switzerland : Springer, 2017  |z 3319552384  |z 9783319552385  |w (OCoLC)972773414 
830 0 |a Archimedes (Dordrecht, Netherlands) ;  |v v. 49. 
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