How Do You Calculate Resulting Velocity Vectors in 3D Collisions?

[MinatureCook]

Hey, I've done quite a bit of Mechanics work in the past... But I really don't even know where to start here.

For some work I'm doing, I need to calculate the resulting velocity vectors when 2 objects collide. These 2 objects can be any shape, any mass and going at any velocity independently. (The simulation is in 3D, so x, y, z)

I suppose I'd have to calculate the normal of the two objects, do something with their velocity vectors and masses... And I suppose it would also depend on the objects' bounciness/stiffness etc...

If anyone could give me the names of some equations I can look into? Or any sort of help... Really just a place to start would be great.

Thanks for any help,
Stephen

 

[AJ Bentley]

Commonly called a Billiard ball collision.

 

[MinatureCook]

I'm Googling that term now, apparently it's also called "Elastic Collision" which is a great help (I had no idea of what to even start searching before) - but all of the equations seem to be confined to a 1D plane of movement.

Would it just be a matter of making the velocity vectors 3D? Here's to hoping so - it's just things rarely are so simple when transferring over to 3 dimensions in Maths

Edit:
Ahh, actually - I just found this Wikipedia article
http://en.wikipedia.org/wiki/Elastic_collision
Which explains about 2D and 3D at the bottom. It's not as simple, but neither is it beyond my knowledge - so I'm happy there :P

Thanks a lot for the help; I genuinely wouldn't have known where to start looking without that

 

[AJ Bentley]

Perfectly OK to just go to 3 dimensions. Or as many as you like ;-)

You just have to resolve the velocities and momenta into 3 orthogonal directions.

Of course, you rarely have to do that in physics problems because any collision between two particles is only in 1 plane, even when it's a glancing collision.

You might want to consider inelastic collision - in the real world things tend to splat more than they bounce.

If it's not a serious project ( a game for example) you could equally well 'fake it'. Just use random direction changes and keep the total momentum/ energy constant (or lose a bit - inelastic). No need to meticulously work out contact angles.