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When you say "all quaternions" did you mean "pure imaginary quaternions"?



Oops, yes I did.

For curious readers: `2` is a quaternion, but `exp(2)` doesn't generate a rotation, it generates 7.389... just like normal exponentiation on reals. So if you have a real term in your lie algebra, it will generate things that scale the object as well as rotating it.

So instead you want only `ai + bj + ck`, as `exp(ai + bj + ck)` will always have magnitude 1




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