- #1
Jhenrique
- 685
- 4
Using http://www.mymathforum.com/download/file.php?id=6171 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?
[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?