The three-body problem and the equations of dynamics : Poincaré's foundational work on dynamical systems theory / Henri Poincaré (deceased) ; translated by Bruce D. Popp.
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 o...
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Full Text (via Springer) |
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| Other title: | Sur le problème des trois corps et les équations de la dynamique. English. |
| Format: | eBook |
| Language: | English French |
| Published: |
Cham, Switzerland :
Springer,
2017.
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| Series: | Astrophysics and space science library ;
443. |
| Subjects: |
Table of Contents:
- Translator's Preface; The Monograph; Errors and Typos; The Translation; References and Index; Notation; Section 4 of Chapter 2, Theorem III; Notable Concepts; Acknowledgements; Bibliography; Author's Preface; Contents; Review; 1 General Properties of the Differential Equations; 1 Notations and Definitions; 2 Calculation of Limits; 3 Application of the Calculation of Limits to Partial Differential Equations; 4 Integration of Linear Equations with Periodic Coefficients; 2 Theory of Integral Invariants; 1 Various Properties of the Equations of Dynamics; 2 Definitions of Integral Invariants.
- 3 Transformation of Integral Invariants4 Using Integral Invariants; 3 Theory of Periodic Solutions; 1 Existence of Periodic Solutions; 2 Characteristic Exponents; 3 Periodic Solutions of the Equations of Dynamics; 4 Calculation of the Characteristic Exponents; 5 Asymptotic Solutions; 6 Asymptotic Solutions of the Equations of Dynamics; Equations of Dynamics and the N-Body Problem; 4 Study of the Case with Only Two Degrees of Freedom; 1 Various Geometric Representations; 5 Study of the Asymptotic Surfaces; 1 Description of the Problem; 2 First Approximation; 3 Second Approximation.
- 4 Third Approximation6 Various Results; 1 Periodic Solutions of the Second Kind; 2 Divergence of Lindstedt's Series; 3 Nonexistence of One-to-One Integrals; 7 Attempts at Generalization; 1 The N-Body Problem; Erratum; Bibliography; Author Index; Subject Index.