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Rotation with 2 angles

  1. Jan 21, 2014 #1
    Using this coordinate system and writing the relationships:

    [tex]\vec{\rho}\;'=R^{-1}(\phi)\vec{\rho}[/tex]
    [tex]\begin{bmatrix} r'\\ z'\\ \end{bmatrix} = \begin{bmatrix} cos(\phi) & sin(\phi)\\ -sin(\phi) & cos(\phi)\\ \end{bmatrix} \begin{bmatrix} r\\ z\\ \end{bmatrix}[/tex]
    and

    [tex]\vec{r}\;'=R(\theta)\vec{r}[/tex]
    [tex]\begin{bmatrix} x'\\ y'\\ \end{bmatrix} = \begin{bmatrix} cos(\theta) & -sin(\theta)\\ sin(\theta) & cos(\theta)\\ \end{bmatrix} \begin{bmatrix} x\\ y\\ \end{bmatrix}[/tex]

    and that ##\vec{r}=\vec{x}+\vec{y}## and ##\vec{\rho}=\vec{r}+\vec{z}##.

    Joinning all these relations, I ask: is possible to join theses two rotations in one unique equation?
     
  2. jcsd
  3. Jan 26, 2014 #2
    Indeed. Express the matrices in the same basis and matrix multiply the compose the rotations.
     
  4. Jan 27, 2014 #3
    Give me an example?
     
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