I'm not quite sure I get the idea of a degree of freedom for a system. First of all: Is there freedom in characterizing the DOF for a system - i.e. will specifying the DOF for a system relative to any coordinate system always be the same? Next let me do an example: If we have 2 particles free to rotate about any axis, what is the total DOF for that system? Is that 12 or 6? Because I normally see 6, but isn't that just because you see the particle as a point? On the other hand it perhaps doesn't make sense to say that a single particle can rotate. Next let's imagine that we put a constraint on the system saying that the distance between the two particles must stay fixed. I have then been told that the total DOF are 5. But how do I realize that? And does this number account for rotational DOF?