The Three-Body Problem三体问题
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作者： Mauri Valtonen，Hannu Karttunen著
出 版 社：
出版时间： 2006-3-1字数：版次：页数： 345印刷时间： 2006/03/01开本： 16开印次：纸张： 胶版纸I S B N ： 9780521852241包装： 精装内容简介
How do three celestial bodies move under their mutual gravitational attraction? This problem has been studied by Isaac Newton and leading mathematicians over the last two centuries. Poincaré's conclusion, that the problem represents an example of chaos in nature, opens the new possibility of using a statistical approach. For the first time this book presents these methods in a systematic way, surveying statistical as well as more traditional methods. This book should be essential reading for students in a rapidly expanding field and is suitable for students of celestial mechanics at advanced undergraduate and graduate level.
作者简介：
Mauri Valtonen is a Professor of Astronomy at the University of Turku.
Hannu Karttunen is a Systems Manager at Tuorla Observatory, University of Turku.
目录
Preface
1 Astrophysics and the three-body problem
1.1About the three-body problem
1.2The three-body problem in astrophysics
1.3Short period comets
1.4Binary stars
1.5Groups of galaxies
1.6Binary black holes
2 Newtonian mechanics
2.1Newton's laws
2.2Inertial coordinate system
2.3Equations of motion for N bodies
2.4Gravitational potential
2.5Constants of motion
2.6The virial theorem
2.7The Lagrange and Jacobi forms of the equations of motion
2.8Constants of motion in the three-body problem
2.9Moment of inertia
2.10 Scaling of the three-body problem
2.11 Integration of orbits
2.12 Dimensions and units of the three-body problem
2.13 Chaos in the three-body problem
2.14 Rotating coordinate system Problems
3 The two-body problem
3.1Equations of motion
3.2Centre of mass coordinate system
3,3Integrals of the equation of motion
3.4Equation of the orbit and Kepler's first law
3.5Kepler's second law
3.6Orbital elements
3.7Orbital velocity
3.8True and eccentric anomalies
3.9Mean anomaly and Kepler's equation
3.10 Solution of Kepler's equation
3.11 Kepler's third law
3.12 Position and speed as functions of eccentric anomaly
3.13 Hyperbolic orbit
3.14 Dynamical friction
3.15 Series expansions Problems
4 Hamiltonian mechanics
4.1Generalised coordinates
4.2Hamiltonian principle
4.3Variational calculus
4.4Lagrangian equations of motion
4.5Hamiltonian equations of motion
4.6Properties of the Hamiltonian
4.7Canonical transformations
4.8Examples of canonical transformations
4.9The Hamilton-Jacobi equation
4.10 Two-body problem in Hamiltonian mechanics: two dimensions
4.11 Two-body problem in Hamiltonian mechanics: three dimensions
4.12 Delaunay's elements
4.13 Hamiltonian formulation of the three-body problem
4.14 Elimination of nodes
4.15 Elimination of mean anomalies Problems
5The planar restricted circular three-body problem and other special cases
5.1Coordinate frames
5.2Equations of motion
5.3Jacobian integral
5.4Lagrangian points
5.5Stability of the Lagrangian points
5.6Satellite orbits
5.7The Lagrangian equilateral triangle
5.8One-dimensional three-body problem Problems
6 Three-body scattering
7 escape in the general three-body problem
8 Dcattering and capture in the general problem
9 Perturbations in hierarchical systems
10 Perturbations in strong three-body encounters
11 Some astrophysical problems
References
Author index
Subject index
