# Rotations with quaternions

1. Feb 26, 2006

### Plott029

If we take a vector "v" and utilize a quaternion q and its conjugate complex, we can rotate the "v" vector this way:

qvq*

The question is, what happens if "v" is not a vector, and is a quaternion? rotates it?

2. Feb 26, 2006

### quasar987

Hi Plott029. In what class are quaternions introduced?

3. Feb 27, 2006

### Plott029

The utilized to rotations (norm 1, etc.). But the problem I see is that in vectors, I can understand it. But if "v" is a quaternion, I don't understand if the answer is a "rotated quaternion" or another thing.

4. Feb 27, 2006

### neurocomp2003

Am i to understand the question is asking what happens if v is a quaternion and not a vector? your wording was a little confusing.

1 method is to find out by expanding the quaternions into there matrix form =].

the 2nd is to just simple understand whats going on...
what happens when you multiple to Qs. Whats does the conjugate
of a quaternion represent

btw is this for a math class or a 3D math/programming class?

5. Feb 27, 2006

### George Jones

Staff Emeritus
I thought that qvq^(-1) gives a rotation of a vector v. If v is a general quaternion, then v = v0 + w, with v0 a scalar and w a vector (pure quaternion). Then

qvq^(-1) = v0 + qwq^(-1).

In some sense this can regarded as a rotation of quaternion: the scalar part is invariant under rotation and the vector part gets rotated as ususal.

Regards,
George

6. Mar 1, 2006

### Plott029

quaternions

this way, the rotation of a quaternion w is, for example, an expresión like this: qwq(-1) ???