# $4D$ rotations and quaternions

I have a question about $4D$ rotation:
I programmed a little $4D$ game and I used the classical hyper-sphere coordinates, to rotate a vector.

It works, but it has some problems:
(just for clarity I take the cartesian coordinates, translate in hypersphere coordinates, add the angle I wish than translate back to cartesian)
This procedure causes jumble locks and approximation errors.

I'm asking you if it is possible like in $3D$ to have quaterinions to manage the rotations?

I'll prefer not to use rotation matrix, which has other problems:

Thanks in advance for the help!
If you want to have a look at the game:
http://www.youtube.com/watch?v=8IUnqm8j4BE
http://www.youtube.com/watch?v=NaeqUp3jbls

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Yes. You can use two quaternions. One acts on the space of all quaternions by left multiplication and the other acts by right multiplication. –  Qiaochu Yuan Aug 21 '11 at 23:43
Here are two related questions: math.stackexchange.com/q/40088 and math.stackexchange.com/q/24739 –  t.b. Aug 22 '11 at 0:35
thank you Theo! the guy really explained it well, I'll try to translate it in my program and if I have other question I'll come back here –  Pella86 Aug 22 '11 at 5:57
For more on what Qiaochu is referring to, see the Wikipedia entry en.wikipedia.org/wiki/… –  Willie Wong Aug 22 '11 at 13:04
I was going to ask this same question mysef, but my previous questions were quoted as references! I am using 4x4 matrix for rotations, but I was looking for something less resource intensive, like quaternions... –  lvella Nov 22 '11 at 14:20