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The Three-Body Problem and the Equations of Dynamics

Poincaré’s Foundational Work on Dynamical Systems Theory

  • Henri Poincaré

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

Table of contents

  1. Front Matter
    Pages i-xxii
  2. Review

    1. Front Matter
      Pages 1-1
    2. Henri Poincaré
      Pages 37-76
    3. Henri Poincaré
      Pages 77-144
  3. Equations of Dynamics and the N-Body Problem

    1. Front Matter
      Pages 145-145
    2. Henri Poincaré
      Pages 161-202
    3. Henri Poincaré
      Pages 203-236
    4. Henri Poincaré
      Pages 237-240
  4. Back Matter
    Pages 241-248

About this book

Introduction

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

Authors and affiliations

  • Henri Poincaré
    • 1
  1. 1.ParisFrance

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-319-52899-1
  • Copyright Information Springer International Publishing AG 2017
  • Publisher Name Springer, Cham
  • eBook Packages Physics and Astronomy
  • Print ISBN 978-3-319-52898-4
  • Online ISBN 978-3-319-52899-1
  • Series Print ISSN 0067-0057
  • Series Online ISSN 2214-7985
  • Buy this book on publisher's site