I am familiar with the mechanics of colliding spheres but I am trying to understand how this generalizes to irregular shapes (eg. 2 cubes colliding in 3D space). Clearly this is a more involved problem since:
There are many ways that the objects can come into contact (face-face, edge-face, edge-edge, vertex-face, etc).
The rotation of the object must be considered as it is not spherically symmetrical.
The centers of mass of the colliding objects will not necessarily be on the line of impact, leading to torque forces.
I understand how to calculate the result of something like a rigid square in a 2D space colliding with a fixed, infinite surface. However, when the surface is instead replaced with another polygon, the problem becomes more difficult.
It also occurs to me that there is a disconnect between the real world and any mathematical system which models perfect geometric shapes (with infinitesimal vertices) which do not really exist in the physical world. Therefore, even when it appears as though a sharp point is colliding with a surface, in the real world there is always a finite contact area. So how does this affect the problem of modelling general collisions?
To be clear, I am not looking for information about collision detection. Actually I was quite frustrated that I was unable to find any material on this subject with a quick google search... One might have expected this to be a standard problem in undergraduate mechanics and yet all I can find online only deals with the collision of spheres.
Is it simply that a problem of this nature is too complex to be explained in terms of the Newtonian formulation of classical mechanics? Would it be a sensible approach to use Lagrangian/Hamiltonian mechanics instead?
If anyone can either give me some insight into how to calculate the result of such collisions, or direct me to some reading material elsewhere, that would be greatly appreciated.
Edit: One may suppose for simplicity/illustration that I would like to model the collision of exactly 2 hard cubes in 3D space that are known to collide at some time but for which the exact point of impact and the velocities/rotation of the cubes could be anything.