Numerical Solutions of the N-Body Problem

Approach your problem from the right It isn't that they can't see end and begin with the answers. the solution. Then one day, perhaps you will find It is that they can't see the the final question. problem. G.K. Chesterton. The Scandal The Hermit Clad in Crane Feathers in of Father Brown The Point of R. van Gulik's The Chinese Maze Murders. a Pin. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new brancheq. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non-trivially) in regional and theoretical economics, algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisci­ fI plines as "experimental mathematics", "CFD , "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes.

Contenu

1. Conventional Numerical Methods For Solving The Initial Value Problem.- 1.1. The Initial Value Problem.- 1.2. Discretization Methods.- 1.3. Survey of Numerical Methods for the Initial Value Problem.- 1.3.1. One-step Methods.- 1.3.2. Linear Multistep Methods.- 1.3.3. Extrapolation Methods.- 1.3.4. Some Other Methods.- 2. The General N-Body Problem.- 2.1. Equations of Motion.- 2.2. The Application of Conventional Numerical Methods.- 2.3. Discrete Mechanics of Greenspan.- 2.3.1. Basic Relations and their Properties.- 2.3.2. Stability and Convergence.- 2.3.3. Practical Realization of Greenspan's Method.- 2.4. Discrete Mechanics of Arbitrary Order.- 2.5. Energy Conserving Methods.- 3. The Relative Motion Of N Bodies.- 3.1. Equations of Motion.- 3.2. The Application of Conventional Numerical Methods.- 3.3. The Application of Discrete Mechanics Formulas.- 4. Equations Of Motion In A Rotating Frame.- 4.1. Equations of Motion.- 4.2. The Application of Conventional Numerical Methods.- 4.3. Discrete Mechanics in a Rotating Frame.- 4.4. A Motion nearby the Equilibrium Points.- 4.5. Discrete Hill's Equations.- Appendix. PL/I Procedures.- References.