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The Three-Body Problem and the Equations of Dynamics: Poincar�'s Foundational Work on Dynamical Systems Theory

The Three-Body Problem and the Equations of Dynamics: Poincar�'s Foundational Work on Dynamical Systems Theory

The Three-Body Problem and the Equations of Dynamics: Poincar�'s Foundational Work on Dynamical Systems Theory
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The Three-Body Problem and the Equations of Dynamics: Poincar�'s Foundational Work on Dynamical Systems Theory

The Three-Body Problem and the Equations of Dynamics: Poincar�'s Foundational Work on Dynamical Systems Theory

Overview

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.

Product Details

ISBN-13: 9783319528984
Publisher: Springer International Publishing
Publication date: 05/12/2017
Series: Astrophysics and Space Science Library , #443
Edition description: 1st ed. 2017
Pages: 248
Product dimensions: 6.10(w) x 9.25(h) x (d)

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.

Table of Contents

Translator's Preface.- Author's Preface.- Part I. Review.- Chapter 1 General Properties of the Differential Equations.- Chapter 2 Theory of Integral Invariants.- Chapter 3 Theory of Periodic Solutions.- Part II. Equations of Dynamics and the N-Body Problem.- Chapter 4 Study of the Case with Only Two Degrees of Freedom.- Chapter 5 Study of the Asymptotic Surfaces.- Chapter 6 Various Results.- Chapter 7 Attempts at Generalization.- Erratum. References.- Index.
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