N-Body Simulation using symplectic integrators

[< Ali >]

TL;DR Summary

Need help on algorithm clarification

Hi,
I hope I am in the right section of the forum. I was trying to understand the following algorithm:

https://benchmarksgame-team.pages.debian.net/benchmarksgame/program/nbody-python3-1.html
and particulary this part:

def advance(dt, n, bodies=SYSTEM, pairs=PAIRS):

    for i in range(n):
        for (([x1, y1, z1], v1, m1),
             ([x2, y2, z2], v2, m2)) in pairs:
            dx = x1 - x2
            dy = y1 - y2
            dz = z1 - z2
            mag = dt * ((dx * dx + dy * dy + dz * dz) ** (-1.5))
            b1m = m1 * mag
            b2m = m2 * mag
            v1[0] -= dx * b2m
            v1[1] -= dy * b2m
            v1[2] -= dz * b2m
            v2[0] += dx * b1m
            v2[1] += dy * b1m
            v2[2] += dz * b1m
        for (r, [vx, vy, vz], m) in bodies:
            r[0] += dt * vx
            r[1] += dt * vy
            r[2] += dt * vz

What are the mag and b1m variables? would be very thankful for any explanations or resources that derives this algorithm.

 

[Ibix]

Can you write it out as a formula? It may be better to go straight to the change in $v_x$.

Hint: $$\cos\theta=\frac{\Delta x}{\sqrt{\Delta x^2+\Delta y^2+\Delta z^2}}$$

 

[< Ali >]

Got it :) Thank you!