Astrophysics and Space Science Library

The Three-Body Problem and the Equations of Dynamics

Poincaré’s Foundational Work on Dynamical Systems Theory

Authors: Poincaré, Henri

  • Provides a clear and accurate translation of Poincaré's work, making it accessible to English-speaking readers who want to study and understand his thinking
  • Includes Poincaré’s entire classic, so readers can hear Poincaré’s own, compelling voice, explore the details and form their own opinions
  • The translator's preface identifies key concepts and their location in the book, facilitating the selection of specific sections for further attention  
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Buy this book

eBook $109.00
price for USA (gross)
  • ISBN 978-3-319-52899-1
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $139.00
price for USA
  • ISBN 978-3-319-52898-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this book

Here is an accurate and readable translation of a seminal article by Henri Poincaré that is a classic in the study of dynamical systems popularly called chaos theory. In an effort to understand the stability of orbits in the solar system, Poincaré applied a Hamiltonian formulation to the equations of planetary motion and studied these differential equations in the limited case of three bodies to arrive at properties of the equations’ solutions, such as orbital resonances and horseshoe orbits. 

Poincaré wrote for professional mathematicians and astronomers interested in celestial mechanics and differential equations. Contemporary historians of math or science and researchers in dynamical systems and planetary motion with an interest in the origin or history of their field will find his work fascinating. 

About the authors

Bruce D. Popp is an ATA-certified translator for French into English with a BA in physics from Cornell University and a PhD in astrophysics from Harvard University. He is also a U.S. Patent and Trademark Office registered patent agent. As a professional translator, he performs premium-quality translations of scientific and technical documents, especially patent applications. As an independent scholar, he is applying his love of astrophysics, mathematics and French to understanding the work of Henri Poincaré. 

Reviews

“In the work under review, Popp, a professional translator, has produced an English translation of Poincaré’s monograph. … This book will be most appropriate for readers with an expressed interest in the history of mathematics and physics or dynamical systems. Summing Up: Recommended. Upper-division undergraduates and above; researchers and faculty.” (M. D. Sanford, Choice, Vol. 55 (4), December, 2017)


Table of contents (7 chapters)

  • General Properties of the Differential Equations

    Poincaré, Henri

    Pages 3-36

  • Theory of Integral Invariants

    Poincaré, Henri

    Pages 37-76

  • Theory of Periodic Solutions

    Poincaré, Henri

    Pages 77-144

  • Study of the Case with Only Two Degrees of Freedom

    Poincaré, Henri

    Pages 147-160

  • Study of the Asymptotic Surfaces

    Poincaré, Henri

    Pages 161-202

Buy this book

eBook $109.00
price for USA (gross)
  • ISBN 978-3-319-52899-1
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $139.00
price for USA
  • ISBN 978-3-319-52898-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
The Three-Body Problem and the Equations of Dynamics
Book Subtitle
Poincaré’s Foundational Work on Dynamical Systems Theory
Authors
Translated by
Popp, B.D.
Series Title
Astrophysics and Space Science Library
Series Volume
443
Copyright
2017
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing AG
eBook ISBN
978-3-319-52899-1
DOI
10.1007/978-3-319-52899-1
Hardcover ISBN
978-3-319-52898-4
Series ISSN
0067-0057
Edition Number
1
Number of Pages
XXII, 248
Number of Illustrations and Tables
9 b/w illustrations
Additional Information
Original French edition published by Institut Mittag-Leffler, Sweden, 1890
Topics