# Need Formula: 2D Relativistic (hopefully) Collisions with COR (e)

1. Apr 21, 2010

### Sunmaz

I need a formula that yields the speed and angle after a 2D collision that uses the coefficient of restitution (e). Preferably this would also be relativistic. I have searched EVERYWHERE for this and could not find it.
To "prove" that I have indeed tried I have read the collision sections of Classical Mechanics by R. Douglas Gregory, Mechanics, Volume 4
By Ted Graham, Aidan Burrows, Brian Gaulter, Physics for Scientists and Engineers, Volume 2
By Lawrence S. Lerner, Impact Mechanics
By W. J. Stronge, Engineering Mechanics: Dynamics
By Russell C. Hibbeler, and MANY more....I have also searched extensively online to no avail. Please find/derive this formula for me! Thanks!

The most useful thing I have found so far is: http://books.google.ca/books?id=oVL...icient of restitution collision angle&f=false

This gives a non-relativistic speed using COR but I need the angle too but not for the scenario I describe (a 2D collision between two spheres) - perhaps someone could also explain how to get that from the formula there. Does the COR only effect v and not the angle? Shouldn't a speed formula be independent of the incident angles (and that be factored in with the calculation of the exiting angle)?

Thank you for any and all help!

Last edited: Apr 21, 2010
2. Apr 22, 2010

### Sunmaz

3. Apr 25, 2010

### Sunmaz

Someone must have something to say regarding this?!

4. Apr 25, 2010

### diazona

Take a look at Wikipedia:
http://en.wikipedia.org/wiki/Coefficient_of_restitution
The article shows the non-relativistic equations for velocity perpendicular to the collision plane, together with the procedure for deriving them, starting from the definition of COR and the law of conservation of momentum. I imagine that you could take those equations, replace the non-relativistic law of conservation of momentum as used in the Wikipedia article with the relativistic one, and derive a relativistic equation for the perpendicular component of velocity in a collision. You should also be able to assume that the parallel component of velocity remains the same, as in NR collisions, and from that obtain the formulas for speed and angle. I wouldn't be surprised if they look pretty ugly, though.

I've written something about a special case of inelastic collisions that you could look at, basically as an example of manipulating the collision equations - but it's not particularly relevant to your situation.
http://www.ellipsix.net/blog/post.84.html

5. Apr 26, 2010

### Sunmaz

Thanks. I was hoping that someone would know it but I guess I'll have to try that.

6. Apr 26, 2010

### Sunmaz

In all honesty I'm not sure I'm mathematically capable of it but I can try :P.

7. Apr 26, 2010

### diazona

Give it a try and post it here, maybe we can help you fix it up. It'll be good learning experience too. (If it's not obvious to you how to do so, I'd suggest first trying to reproduce the collision equations given on the Wikipedia page as practice.)

8. Apr 26, 2010

### Sunmaz

I will follow your advice and post it here when I get the time (hopefully within the next week and a half). I looked at what you wrote and it is very well written and quite enlightening (although like you said it is not of much use to me). Thanks for the advice and well done!