CSC/ECE 506 Spring 2011/ch4a zz

Introduction

The N-body problem stated as follows: Select the position and velocity of n celestial bodies as states. Given the initial condition of of N bodies, compute their states at arbitrary time T. Normally a three-dimensional space is considered for N-body problem.

Many mathematician proofed that the n-body problem is unsolvable analytically. [2]

The most common, and simplest, approach is to iterate over a sequence of small time steps. Within each time step, the acceleration on a body is approximated by the instantaneous acceleration at the beginning of the time step. The instantaneous acceleration on a single body can be directly computed by summing the contributions from each of the other N ÿ 1 particles. While this method is conceptually simple, vectorizes well, and is the algorithm of choice for many applications, its O…N2† arithmetic complexity rules it out for large-scale simulations involving millions of particles.

This type of applications simulate interactions among a set of bodies (also called particles from now on) confined into a space region, and exposed to a certain force field.Their application field is really wide, and they can be used from simulation of celestial bodies (gravitational interaction)to interactions of a set of particles (electromagnetic interaction)

References

[1] [1] Collection of remarkable three-body motions

[2] Diacu, F (01/01/1996). "The solution of the n-body problem". The Mathematical intelligencer (0343-6993), 18 (3), p. 66.