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The Three-Body Problem and the Equations of Dynamics

Poincaré’s Foundational Work on Dynamical Systems Theory

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  • 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

  • Includes supplementary material: sn.pub/extras

Part of the book series: Astrophysics and Space Science Library (ASSL, volume 443)

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  • ISBN: 978-3-319-52899-1
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  • Tax calculation will be finalised during checkout
Softcover Book
USD 159.99
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Table of contents (7 chapters)

  1. Front Matter

    Pages i-xxii
  2. Review

    1. Front Matter

      Pages 1-1
    2. Theory of Integral Invariants

      • Henri Poincaré
      Pages 37-76
    3. Theory of Periodic Solutions

      • Henri Poincaré
      Pages 77-144
  3. Equations of Dynamics and the N-Body Problem

    1. Front Matter

      Pages 145-145
    2. Study of the Asymptotic Surfaces

      • Henri Poincaré
      Pages 161-202
    3. Various Results

      • Henri Poincaré
      Pages 203-236
    4. Attempts at Generalization

      • Henri Poincaré
      Pages 237-240
  4. Back Matter

    Pages 241-248

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. 

Keywords

  • Dynamical Systems Theory
  • Hamiltonian Formulation of Celestial Mechanics
  • Contactless Surface
  • Integral Invariant
  • Recurrence Theorem
  • Poincare Section
  • Orbital Resonance
  • Horseshoe Orbits
  • Origin of Phase Space
  • Doubly Asymptotic Solutions

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)

Authors and Affiliations

  • Paris, France

    Henri Poincaré

About the author

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. 

Bibliographic Information

Buying options

eBook
USD 119.00
Price excludes VAT (USA)
  • ISBN: 978-3-319-52899-1
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD 159.99
Price excludes VAT (USA)
Hardcover Book
USD 159.99
Price excludes VAT (USA)