Introduction / 1: |
History / 1.1: |
Global vs. Local Notation / 1.2: |
Summary of Chapters / 1.3: |
Further R eading / 1.4: |
Equations of Celestial Mechanics / 2: |
N-Body Problem / 2.1: |
The Kepler Problem / 2.2: |
R estricted Problem / 2.3: |
Hill's Lunar Equations / 2.4: |
Elliptic Problem / 2.5: |
Problems / 2.6: |
Hamiltonian Systems / 3: |
Symplectic Coordinates / 3.1: |
Generating Functions / 3.3: |
R otating Coordinates / 3.4: |
Jacobi Coordinates / 3.5: |
Action-Angle and Polar Coordinates / 3.6: |
Solution of the Kepler Problem / 3.7: |
Spherical Coordinates / 3.8: |
Symplectic Scaling / 3.9: |
Central Configurations / 3.10: |
Equilibrium Solutions / 4.1: |
Equations for a Central Configuration / 4.2: |
Relative Equilibrium / 4.3: |
Lagrangian Solutions / 4.4: |
Euler-Moulton Solutions / 4.5: |
Central Configuration Coordinates / 4.6: |
Symmetries,Integrals,and Reduction / 4.7: |
Group Actions and Symmetries / 5.1: |
Systems with Integrals / 5.2: |
Noether's Theorem / 5.3: |
Integrals / 5.4: |
Symplectic R eduction / 5.5: |
Reducing the N-Body Problem / 5.6: |
Theory of Periodic Solutions / 5.7: |
Equilibrium Points / 6.1: |
Fixed Points / 6.2: |
Periodic Differential Equations / 6.3: |
Autonomous Systems / 6.4: |
Systems with Symmetries / 6.5: |
Hamiltonian Systems with Symmetries / 6.7: |
Satellite Orbits / 6.8: |
Main Problem for Satellite Problem / 7.1: |
Continuation of Solutions / 7.2: |
The Restricted Problem / 7.3: |
Main Problem for the Three-Bodies / 8.1: |
Continuation of Periodic Solutions / 8.2: |
Bifurcations of Periodic Solutions / 8.3: |
Main Problem for (N + l)-Bodies / 8.4: |
R eduction / 8.5: |
Lunar Orbits / 8.6: |
Main Problem / 9.1: |
Continuation / 9.2: |
Comet Orbits / 9.3: |
Jacobi Coordinates and Scaling / 10.1: |
Kepler Problem / 10.2: |
R educed Space / 10.3: |
The Elliptic Problem / 10.5: |
Apollonius Coordinates / 12.1: |
Symmetries and R eduction / 12.2: |
References / 12.5: |
Index |
Introduction / 1: |
History / 1.1: |
Global vs. Local Notation / 1.2: |
Summary of Chapters / 1.3: |
Further R eading / 1.4: |
Equations of Celestial Mechanics / 2: |