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I have recently been interested in the problem of 2- and 3-dimensional elastic collisions. I just don't understand how to solve these problems analytically: in the 2D case we have 4 variables (x,y components of the velocity times 2 bodies) and only 3 equations (2 conservation of momentum, 1 conservation of energy); in the 3D case (similarly) we have 6 variables and only 4 equtions.

I ran across this page: http://www.plasmaphysics.org.uk/collision2d.htm

but I stopped understanding when they started talking about theta as the sum of two other angles.

I would be happy if somebody could explain it to me.

Thanks a lot!