Design of a Mechanical N-Body Integrator
Ben Leimkuhler
This document describes a gravitational N-body integration algorithm incorporating the following features: (1) it is exactly (neglecting rounding errors) time-reversible, (2) angular and linear momentum are conserved, (3) smooth switching functions are used to split potential terms into local and weak parts so that weaker long-range forces are evaluated relatively rarely and close interactions are identified, (4) close approaches between bodies are resolved accurately, using an efficient integration method, (5) the stepsize varies automatically based on an appropriate Sundman time reparameterization. Although this method is formally second order, the most intensive computations (the close approach dynamics) are executed at higher order, thus improving the overall accuracy of the scheme.