Wikipedia:Reference desk/Archives/Mathematics/2014 December 5
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December 5
editProblem with single rotation in SO(4) using quaternions
editRe. the article Rotations in 4-dimensional Euclidean space, I'm having a problem with a single rotation. Suppose I have a unit quaternion QL=[a,b,c,d]. In the article it states "In quaternion notation, a rotation in SO(4) is a single rotation if and only if QL and QR are conjugate elements of the group of unit quaternions." So if I want to rotate a point at r=[0,0,0,1] (i.e. a point displaced 1 unit along the z axis), the rotated point will be:
which means that the point can never be rotated into the u dimension, it must be constrained to the xyz space. This seems wrong, one should be able to rotate [0,0,0,1] into the u dimension.PAR (talk) 16:50, 5 December 2014 (UTC)
- I concur that it's wrong as written. The correct condition is that there is a unit quaternion a such that QL^* a = a QR. Sławomir Biały (talk) 17:32, 5 December 2014 (UTC)
- Is there a short explanation for your statement? Does that mean (since a*=a-1) that for any two unit quaternions QL and a, that is a single rotation? Thanks for any help... PAR (talk) 05:31, 6 December 2014 (UTC)