Archimedes

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

Authors: Ginoux, Jean-Marc

  • Offers the very first history of nonlinear oscillations
  • Supports understanding of the approach to many mathematical problems of engineering
  • Provides a thorough and clear documentation of this vital piece of the history of mathematical science
  • Presents a vast iconography, an index and many useful references
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eBook $139.00
price for USA in USD (gross)
  • ISBN 978-3-319-55239-2
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $179.99
price for USA in USD
  • Customers within the U.S. and Canada please contact Customer Service at 1-800-777-4643, Latin America please contact us at +1-212-460-1500 (Weekdays 8:30am – 5:30pm ET) to place your order.
  • Due: May 18, 2017
  • ISBN 978-3-319-55238-5
  • Free shipping for individuals worldwide
Softcover $179.99
price for USA in USD
  • ISBN 978-3-319-85604-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

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.

Table of contents (14 chapters)

  • From the Series-Dynamo Machine to the Singing Arc: Gérard-Lescuyer, Blondel, Poincaré

    Ginoux, Jean-Marc

    Pages 3-37

  • The Great War and the First Triode Designs: Abraham, Bloch, Blondel, Van der Pol

    Ginoux, Jean-Marc

    Pages 39-65

  • Van der Pol’s Prototype Equation: Existence and Uniqueness of the Periodic Solution Cartan, Van der Pol, Liénard

    Ginoux, Jean-Marc

    Pages 67-101

  • Van der Pol’s Lectures: Towards the Concept of Relaxation Oscillations

    Ginoux, Jean-Marc

    Pages 109-130

  • Andronov’s Notes: Toward the Concept of Self-Oscillations

    Ginoux, Jean-Marc

    Pages 131-144

Buy this book

eBook $139.00
price for USA in USD (gross)
  • ISBN 978-3-319-55239-2
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $179.99
price for USA in USD
  • Customers within the U.S. and Canada please contact Customer Service at 1-800-777-4643, Latin America please contact us at +1-212-460-1500 (Weekdays 8:30am – 5:30pm ET) to place your order.
  • Due: May 18, 2017
  • ISBN 978-3-319-55238-5
  • Free shipping for individuals worldwide
Softcover $179.99
price for USA in USD
  • ISBN 978-3-319-85604-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
History of Nonlinear Oscillations Theory in France (1880-1940)
Authors
Series Title
Archimedes
Series Volume
49
Copyright
2017
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing AG
eBook ISBN
978-3-319-55239-2
DOI
10.1007/978-3-319-55239-2
Hardcover ISBN
978-3-319-55238-5
Softcover ISBN
978-3-319-85604-9
Series ISSN
1385-0180
Edition Number
1
Number of Pages
XXXVII, 381
Number of Illustrations
73 b/w illustrations, 44 illustrations in colour
Topics