Gravitational Few-Body Dynamics
Using numerical integration, it is possible
to predict the individual motions of a group of a few celestial objects interacting with each other gravitationally. In this
introduction to the few-body problem, a key figure in developing more efficient methods over the past few decades summarizes
and explains them, covering both basic analytical formulations and numerical methods. The mathematics required for celestial
mechanics and stellar dynamics is explained, starting with two-body motion and progressing through classical methods for planetary
system dynamics. This first part of the book can be used as a short course on celestial mechanics. The second part develops
the contemporary methods for which the author is renowned - symplectic integration and various methods of regularization.
This volume explains the methodology of the subject for graduate students and researchers in celestial mechanics and astronomical
dynamics with an interest in few-body dynamics and the regularization of the equations of motion.
1. The problems; 2. Two-body motion; 3. Analytical tools; 4. Variation of parameters; 5. Numerical integration; 6. Symplectic
integration; 7. KS-regularization; 8. Algorithmic regularization; 9. Motion in the field of a black hole; 10. Artificial satellite
orbits; References; Index.
This introduction to the few-body problem progresses from two-body motion and classical
planetary dynamics to modern numerical methods.