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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
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
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
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)
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
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
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
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)
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