The Three-Body Problem and the Equations of Dynamics

Poincaré's Foundational Work on Dynamical Systems Theory
1. Auflage 2017
ISBN: 978-3-319-52898-4
Verlag: Springer International Publishing

Buch, Englisch, Band 443, 248 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 5325 g

Reihe: Astrophysics and Space Science Library

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. 

Zielgruppe

Graduate

Autoren/Hrsg.

Poincaré, Henri

Weitere Mitwirkende

Popp, Bruce D

Fachgebiete

• Naturwissenschaften Astronomie Sonnensystem: Sonne und Planeten
• Naturwissenschaften Physik Angewandte Physik Astrophysik
• Naturwissenschaften Physik Angewandte Physik Statistische Physik, Dynamische Systeme
• Mathematik | Informatik Mathematik Geometrie Dynamische Systeme
• Naturwissenschaften Physik Physik Allgemein Geschichte der Physik

Inhaltsverzeichnis

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.

Über Autor(innen)

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.