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Rotations with quaternions

  1. Feb 26, 2006 #1
    If we take a vector "v" and utilize a quaternion q and its conjugate complex, we can rotate the "v" vector this way:


    The question is, what happens if "v" is not a vector, and is a quaternion? rotates it?
  2. jcsd
  3. Feb 26, 2006 #2


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    Hi Plott029. In what class are quaternions introduced?
  4. Feb 27, 2006 #3
    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.
  5. Feb 27, 2006 #4
    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?
  6. Feb 27, 2006 #5

    George Jones

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    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.

  7. Mar 1, 2006 #6

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