TY  - BOOK
AU  - Poincaré,Henri
TI  - Three-Body Problem and the Equations of Dynamics: Poincaré's Foundational Work on Dynamical Systems Theory 
T2  - Astrophysics and Space Science Library,
SN  - 9783319528991
U1  - 515.39 P755T 23
PY  - 2017///
CY  - Switzarland
PB  - Springer-Nature
KW  - Astrophysics
KW  - Dynamics
KW  - Ergodic theory
KW  - Physics
KW  - Planetary science
KW  - Statistical physics
KW  - Dynamical Systems and Ergodic Theory
KW  - Astrophysics and Astroparticles
KW  - History and Philosophical Foundations of Physics
KW  - Planetary Sciences
KW  - Statistical Physics and Dynamical Systems
N1  - 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
N2  - 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
ER  -