I am currently developing a simulation that involves sphere (or if you like particle) collision in 3D space. And I want it to be accurate (on the level of classic mechanics).
The algorithm to do the job would take in the velocities, masses and relative position (aka line of impact) of two colliding particles and compute their new velocities short after the collision.
So I tried to develop this algorithm and ran into a problem.
I set up the equations for the conservation of momentum and conservation of kinetic energy.
That gave me four equations, one for the kinetic energy (scalar) and three for the momentum (one for each of the three dimensions).
Since the result of this calculation has six variables (the two new velocity vectors) it needs six equations to be solved. Obviously two more are necessary. I dont know how to set them up but they certainly have to take the relative position into account.
Well, I just hope that someone here can help me solve this.
In case I have left something unclear, just ask.