> It seems [1-4] means there's 4 URLs where you replace [1-4] with a number 1 to 4 inclusive.

Heh, yes, thought that was obvious, sorry
Been doing regexp searches too often, I guess...

If a vector is conserved, then so is its norm. If the velocity vector is conserved, then so must the quantity you call speed (which is the root of the norm of the velocity vector).

How are you calculating it?

BTW. I've never seen the convention that `speed == magnitude of velocity vector' before.

EDIT: I made a slightly different (but easier) analisys than I originally proposed. It is based on the assertion that the momentum can be split in two parts: one along the surface normal at the point of collision, one perpendicular to it.
The first changes in the colission, while the latter is not.

You can have a look at my (handwritten, beware!) work at
http://gene.science.uva.nl/~eglebbk/twosphere.png

HTH

Evert, you're confusing the relative velocity with the sum of velocities. Obviously, a constant sum of velocities does not imply a constant sum of speeds (like Orz's calculation demonstrates). A dramatic demonstration of this is when two perfectly inelastic objects collide head-on. Total speed goes from positive to zero.
BTW, if the collisions ARE elastic then there is an additional constraint of the sum of the squares of the speeds remaining constant.

Ehm... I don't think so. Where am I doing that?

I'll reiterate what I said above and try to make more clearly what I meant. It seems there is a confusion between two things here.

I said that if the velocity vector is conserved, then so is its norm (I won't call it speed, since that is confusing to me).
What I did not (mean) to claim is that the sum of norms of individual velocities is conserved.

As far as I know, this sum has no physical meaning anyway, so it doesn't matter.

Obviously. The same holds for any other system that has energy dissipation. I don't think I ever claimed otherwise, as the case we were discussing involves elastic collision.

This is the same as I said above: the total velocity vector is conserved, therefor, so is its norm (and therefor also the squared norm).

I think the calculations I made (follow the link in my previous post if you want to see them) cover this case for two spheres. I'd be interested in some comments, though

Ehm... it looks like we have been essentially saying the same thing to each other, except in wording that caused some confusion (at least for me).

However, I think I disagree now

Your #1 is conservation of momentum, while #2 is conservation of kinetic energy. #2 does not hold in inelastic collissions, since some of the kinetic energy is converted to heat.

I should probably make a demo program to test the equations I derived on paper, but I don't have time at the moment (studying for an exam tomorrow::))

Ugh, my physics is really rusty. Actually it's s more like my basic algebra is rusty... hmm, probably closer to broken. I appologize for posing such half-baked responses. I got the two conservation formulae from my head, but just copied the final from the web.

You're completely right. The formula I gave assumes that object 2 is initially at rest. So, yeah, it's no good. But it should be simple enough to just compute the correct formula using the two conservation formulae.

Ok.. I've gotten a bit further on my game engine and am about to implement damage. When an object hits the player spaceship, I want the resulting damage to be directly proportional to the "force" in the collision. I realize that in the real world it wouldn't be a totally elastic collision if the spaceship aquired damage, but ignore that aspect.

How would you correctly calculate this "impact force" (getting the formula might help me understand the collision code better as well. I grew kinda tired of ball collisions and haven't looked at the code since I copied Orz )?

Ulfalizer

Check my calculations. I think you'll find your answer basically in them.

You need the projection of the momentum vector along the surface normal at the point of collission.