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And what I find harder to understand, why is it that a holonomic constraint allows you to remove a degree of freedom? Consider for instance two particles between which the distance is fixed. This gives 5 degrees of freedom, at least so I heard. Because that is kind of weird to me. As far as I see it the particles can still move anywhere on the x,y and z axis can't they? I can see that in terms of rotations you can only make 2 different ones, and then you can translate the two particles in 3 different directions. But when is it that rotations comes into the picture, because for a collection of N particles you would just have 3N dof, which correspond to movement in three different directions in a euclidean coordinate system.

Talking about the problem with 2 particles with constant distance between them, is it then possible directly, mathematically from the constrain r=c to show that only 5 dof are needed? And can anyone do it?