Direct integration methods of the N-body problem (N-body gravitational problem direct integration techniques, discussing fourth order polynomial method, computer algorithm and regularization procedure for two body encounters and close binaries)

• Published in: Astrophysics and space science Vol. 14; pp. 118 - 132
• Main Author: Aarseth, A J
• Format: Journal Article
• Language: English
• Published: 01.11.1971
• ISSN: 0004-640X
• DOI: 10.1007/BF00649199

A fourth-order polynomial method for the integration of N-body systems is described in detail together with the computational algorithm. Most particles are treated efficiently by an individual time-step scheme but the calculation of close encounters and persistent binary orbits is rather time-consuming and is best performed by special techniques. A discussion is given of the Kustaanheimo-Stiefel regularization procedure which is used to integrate dominant two-body encounters as well as close binaries. Suitable decision-making parameters are introduced and a simple method is developed for regularizing an arbitrary number of simultaneous two-body encounters.