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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
1.1 About the three-body problem
1.2 The three-body problem in astrophysics
1.3 Short period comets
1.4 Binary stars
1.5 Groups of galaxies
1.6 Binary black holes
2 Newtonian mechanics
2.1 Newton's laws
2.2 Inertial coordinate system
2.3 Equations of motion for N bodies
2.4 Gravitational potential
2.5 Constants of motion
2.6 The virial theorem
2.7 The Lagrange and Jacobi forms of the equations of motion
2.8 Constants of motion in the three-body problem
2.9 Moment 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
3.1 Equations of motion
3.2 Centre of mass coordinate system
3,3 Integrals of the equation of motion
3.4 Equation of the orbit and Kepler's first law
3.5 Kepler's second law
3.6 Orbital elements
3.7 Orbital velocity
3.8 True and eccentric anomalies
3.9 Mean 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
4.1 Generalised coordinates
4.2 Hamiltonian principle
4.3 Variational calculus
4.4 Lagrangian equations of motion
4.5 Hamiltonian equations of motion
4.6 Properties of the Hamiltonian
4.7 Canonical transformations
4.8 Examples of canonical transformations
4.9 The 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
5 The planar restricted circular three-body problem and other special cases
5.1 Coordinate frames
5.2 Equations of motion
5.3 Jacobian integral
5.4 Lagrangian points
5.5 Stability of the Lagrangian points
5.6 Satellite orbits
5.7 The Lagrangian equilateral triangle
5.8 One-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
1 Astrophysics and the three-body problem
1.1 About the three-body problem
1.2 The three-body problem in astrophysics
1.3 Short period comets
1.4 Binary stars
1.5 Groups of galaxies
1.6 Binary black holes
2 Newtonian mechanics
2.1 Newton's laws
2.2 Inertial coordinate system
2.3 Equations of motion for N bodies
2.4 Gravitational potential
2.5 Constants of motion
2.6 The virial theorem
2.7 The Lagrange and Jacobi forms of the equations of motion
2.8 Constants of motion in the three-body problem
2.9 Moment 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
3.1 Equations of motion
3.2 Centre of mass coordinate system
3,3 Integrals of the equation of motion
3.4 Equation of the orbit and Kepler's first law
3.5 Kepler's second law
3.6 Orbital elements
3.7 Orbital velocity
3.8 True and eccentric anomalies
3.9 Mean 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
4.1 Generalised coordinates
4.2 Hamiltonian principle
4.3 Variational calculus
4.4 Lagrangian equations of motion
4.5 Hamiltonian equations of motion
4.6 Properties of the Hamiltonian
4.7 Canonical transformations
4.8 Examples of canonical transformations
4.9 The 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
5 The planar restricted circular three-body problem and other special cases
5.1 Coordinate frames
5.2 Equations of motion
5.3 Jacobian integral
5.4 Lagrangian points
5.5 Stability of the Lagrangian points
5.6 Satellite orbits
5.7 The Lagrangian equilateral triangle
5.8 One-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
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