ISBN: 3-540-66630-3
TITLE: Periodic Solutions of the N-Body Problem
AUTHOR: Meyer, Kenneth R.
TOC:

1. Introduction 1
1.1 History 1
1.2 Global vs. Local Notation 4
1.3 Summary of Chapters 6
1.4 Further Reading 8
2. Equations of Celestial Mechanics 9
2.1 N-Body Problem 9
2.2 The Kepler Problem 11
2.3 R estricted Problem 12
2.4 Hill's Lunar Equations 16
2.5 Elliptic Problem 17
2.6 Problems 17
3. Hamiltonian Systems 19
3.1 Hamiltonian Systems 19
3.2 Symplectic Coordinates 20
3.3 Generating Functions 22
3.4 Rotating Coordinates 24
3.5 Jacobi Coordinates 25
3.6 Action-Angle and Polar Coordinates 30
3.7 Solution of the Kepler Problem 31
3.8 Spherical Coordinates 34
3.9 Symplectic Scaling 36
3.10 Problems 37
4. Central Configurations 39
4.1 Equilibrium Solutions 39
4.2 Equations for a Central Configuration 39
4.3 Relative Equilibrium 41
4.4 Lagrangian Solutions 42
4.5 Euler-Moulton Solutions 43
4.6 Central Configuration Coordinates 45
4.7 Problems 49
5. Symmetries, Integrals, and Reduction 51
5.1 Group Actions and Symmetries 53
5.2 Systems with Integrals 60
5.3 Noether's Theorem 61
5.4 Integrals 63
5.5 Symplectic Reduction 64
5.6 Reducing the N-Body Problem 66
5.7 Problems 70
6. Theory of Periodic Solutions 71
6.1 Equilibrium Points 71
6.2 Fixed Points 73
6.3 Periodic Differential Equations 75
6.4 Autonomous Systems 76
6.5 Systems with Integrals 79
6.6 Systems with Symmetries 83
6.7 Hamiltonian Systems with Symmetries 85
6.8 Problems 85
7. Satellite Orbits 87
7.1 Main Problem for Satellite Problem 87
7.2 Continuation of Solutions 89
7.3 Problems 90
8. The Restricted Problem 91
8.1 Main Problem for the Three-Bodies 92
8.2 Continuation of Periodic Solutions 96
8.3 Bifurcations of Periodic Solutions 98
8.4 Main Problem for (N + l)-Bodies 100
8.5 Reduction 101
8.6 Continuation of Periodic Solutions 102
8.7 Problems 102
9. Lunar Orbits 105
9.1 Main Problem 105
9.2 Continuation 107
9.3 Problems 110
10. Comet Orbits 111
10.1 Jacobi Coordinates and Scaling 111
10.2 Kepler Problem 112
10.3 Main Problem 113
10.4 Reduced Space 115
10.5 Continuation 116
10.6 Problems 117
11. Hill's Lunar Equations 119
11.1 Main Problem 120
11.2 Continuation 125
11.3 Problems 126
12. The Elliptic Problem 129
12.1 Apollonius Coordinates 130
12.2 Relative Equilibrium 132
12.3 Main Problem 133
12.4 Symmetries and Reduction 135
12.5 Continuation 136 
12.6 Problems 137
References 138
Index 143
END
