How Does Quaternion Rotation Affect Another Quaternion?

[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?

 

[quasar987]

Hi Plott029. In what class are quaternions introduced?

 

[Plott029]

Hi Plott029. In what class are quaternions introduced?

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.

 

[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 what's 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?

 

[George Jones]

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?

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

 

[Plott029]

quaternions

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