Creating a Particle Collision Simulator

I've decided to create a particle collision simulator durring this summer as a pet coding project to hone my C programming skills.

My hope is to, eventually, have a system that can simulate thermo-dynamic systems ranging from airfoils to sterling engines. But first I need to get the basics down and be able to detect particle collisions and recalculate particle velocities and positions.

Below: a description of the theoretical underpinnings of particle collision detection.

You can check up on the project at the google code page I created.