For a continuous rotation representation in 3D, do you need at least 4 real variables?

Question

I'm pretty sure I have read this somewhere, but I just can't get to find this theorem anywhere.

Is there a theorem that states that for a continuous rotation representation you need at least 4 real variables?

The intuition that shows you don't need more than three variables is: a rotation in 3d is defined by an axis, and an amount of rotation around the axis. The axis itself is determined by specifying a single point on the unit sphere, so requires at most a latitude and a longitude, two variables. The amount of rotation is of course at most one variable; that makes no more than three. — MJD, Mar 27 '23 at 16:20
Thanks for your input! I was mostly interested in finding the explanation of why 3 variables, even though they are enough, are not perfectly continuous and without singularities on the whole domain. — ebernardes, Mar 28 '23 at 07:38

score 1 · Accepted Answer · answered Mar 27 '23 at 14:57

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Turns out, I found what I was looking for! Instead of putting the explanation, I'll rather leave the paper where I found my answer:

answered Mar 27 '23 at 14:57

ebernardes

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Thanks for taking the trouble to come back and answer your own question. – MJD Mar 27 '23 at 16:22

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