Oblique collisions in classical gas I am trying to simulate the collisions in classical gas. So the particles are point like and have identical mass. It is easy to find who collides with whom but the what happens to the particles after they collide is bit tricky. 
Since if the collision were to be only head-on the energy distribution of particles will not change, only their momentum and energy will get exchanged.
Certainly I need to include the oblique collisions in order to change the distribution. So my question is how to accomplish the oblique collisions for the point particles?
 A: The only way to achieve that is to recognize that they are not really point particles. Once you treat them as (small) spheres, you can compute the momentum exchange as a function of lateral offset between them. Some details of the calculation are given in this earlier answer
The math is the same regardless of the size of the spheres - that is, the ratio of probabilities of an almost-head-on vs a slightly-oblique vs a very-oblique collision will be the same; this means that once you normalize to the "total probability of a collision", the actual size of the particles becomes irrelevant.
A: In the center of mass frame of the colliding particles, rotate one particle's velocity vector's x-component by x degrees, y-component by y degrees, z-component by z degrees. 
Then rotate other particle's velocity vector's x-component by -x degrees, y-component by -y degrees, z-component by -z degrees. 
x,y,z are random numbers.
(Physical interpretation of that: the particles fused, then the fusion product fissioned, two identical parts flying into opposite directions)
