Solar System Dynamics

by Carl D. Murray and Stanley F. Dermott

Chapter 8

Resonant Perturbations

1. Structure of the Solar System
2. The Two-Body Problem
3. The Restricted Three-Body Problem
4. Tides, Rotation and Shape
5. Spin-Orbit Coupling
6. The Disturbing Function
7. Secular Perturbations
8. RESONANT PERTURBATIONS
   1. Introduction
   2. The geometry of resonance
      • Figures 8.1-3 : notebook
      • Figure 8.4ac : notebook
      • Figure 8.4bd : notebook
   3. The physics of resonance
   4. Variation of orbital elements
   5. Resonance in the circular restricted three-body problem
      • Table 8.5 : notebook
   6. The pendulum model
   7. Libration width
      • Figure 8.7 : notebook
   8. The Hamiltonian approach
      • Figure 8.8 : notebook
      1. The e and e' resonances
         • Figures 8.9-11 : notebook
      2. The e², e'², I² and I'² resonances
         • Figure 8.12 : notebook
      3. The e³ and e'³ resonances
         • Figure 8.13 : notebook
      4. The ee' and II' resonances
         • Figures 8.14a-c : notebook
         • Figures 8.14d-f : notebook
         • Figures 8.14g-i : notebook
         • Figure 8.15 : notebook
   9. The 2:1 resonance
      1. Exact resonance
      2. Medium amplitude libration
      3. Large amplitude libration
      4. Apocentric libration
      5. Internal circulation
      6. External circulation
      7. Other types of motion
      8. Comparison with analytical theory
   10. The 3:1 and 7:4 resonances
   11. Additional resonances and resonance splitting
   12. Resonant encounters
       • Resonant capture : animation
       • Figure 8.22 : notebook
       • Figure 8.23 : notebook
       • Figure 8.24 : notebook
       • Figures 8.25-28 : notebook
       1. Encounters with first-order resonances
       2. Encounters with second-order resonances
   13. The dynamics of capture and evolution in resonance
   14. Two-body resonances in the solar system
       1. The Titan-Hyperion resonance
       2. The Mimas-Tethys resonance
   15. Resonant encounters in satellite systems
       • Orbital evolution : animation
       • Figure 8.29a : notebook
       • Figure 8.29b : notebook
   16. Three-body resonance
   17. The Laplace resonance
       • Figure 8.30 : notebook
   18. Secular and resonant motion
   19. LONGSTOP Uranus
   20. Pulsar planets
   21. Exercises
       • Answers (PDF)
9. Chaos and Long-term Evolution
10. Planetary Rings

1. Appendix - Solar System Data
2. Appendix - Expansion of the Disturbing Function
3. References (PDF)

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