Program Documentation for N-body Force Calculation

This set of programs calculates the force between N particles according to Newton's Law of Gravitation. This calculation is the kernel of particle simulation codes.

Given N particles, P1 ... PN with positions X1 ... XN in 3-D space, the force on particle Pi due to particle Pj is:

     Fij = G * Mi * Mj * ((Xj - Xi)/Rij^3).

where G is the gravitational constant, Mi is the mass of particle Pi, and Rij is the Euclidean distance between particles Pi and Pj. This program calculates the force on Pi due to all other particles, which is the sum of the forces of all other particles. Note that this law is symmetrical in Pi and Pj except for sign, i.e.

     Fij = - Fji

so that the number of force calculations per pair of particles is (N squared - N)/2.

The particles are represented by a 7 x NN array, p, with initial masses and positions and space for calculating the force.

p	   1        Particle number i -->	NN
	   +-------------------------------------+
 p(MM,:)   |					 |  mass
 p(PX,:)   |					 |  x dim of position
 p(PY,:)   |					 |  y dim of position
 p(PZ,:)   |					 |  z dim of position
 p(FX,:)   |					 |  x dim of force
 p(FY,:)   |					 |  y dim of force
 p(FZ,:)   |					 |  z dim of force
	   +-------------------------------------+

All particle arrays are allocated up to NN, the variable npts is the
actual number of particles used.  Other arrays:

 q (0:6,0:NN-1) - holds a copy of particle information to assist in
	calculating symmetric forces
 dx,dy,dz (0:NN-1) - difference between positions of two particles
 dist,sq,fac (0:NN-1) - distance,distance squared between 2 particles,
		and the factor of multiplication
 tx,ty,tz (0:NN-1) - force calculated between 2 particles
	
The programs initialize p with the mass and positions of npts particles
and result in forces calculated in p.

This documentation prepared by Nancy McCracken, njm@npac.syr.edu.