The Three-Body Problem and the Equations of Dynamics
Springer International Publishing (Verlag)
978-3-319-85012-2 (ISBN)
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.
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.
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.
"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)
| Erscheinungsdatum | 05.03.2022 |
|---|---|
| Reihe/Serie | Astrophysics and Space Science Library |
| Übersetzer | Bruce D Popp |
| Zusatzinfo | XXII, 248 p. 9 illus. |
| Verlagsort | Cham |
| Sprache | englisch |
| Original-Titel | Sur le problème des trois corps et les équations de la dynamique |
| Maße | 155 x 235 mm |
| Gewicht | 421 g |
| Themenwelt | Mathematik / Informatik ► Informatik ► Theorie / Studium |
| Mathematik / Informatik ► Mathematik ► Angewandte Mathematik | |
| Schlagworte | Contactless Surface • Doubly Asymptotic Solutions • Dynamical systems theory • Hamiltonian Formulation of Celestial Mechanics • Horseshoe Orbits • Integral Invariant • Orbital Resonance • Origin of Phase Space • Poincare Section • Recurrence Theorem |
| ISBN-10 | 3-319-85012-1 / 3319850121 |
| ISBN-13 | 978-3-319-85012-2 / 9783319850122 |
| Zustand | Neuware |
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