I have a simple question.
Find the matrix for the rotation of $90^\circ$ counter-clockwise around the vector $v = (1,2,2)$
My first approach here was to create $3$ vectors, $(1,0,0),(0,1,0),(0,0,1)$ and see how a $90^\circ$ rotation effected them. Then take the matrix of that times the vector in this question. However, that seems to be wrong.
Can anyone show me how to do this?
/John.
Best Answer
With Rodrigues formula you have:
$R(v,\theta)=I+\sin(\theta)S(v)+(1-\cos(\theta))S^2(v)$
where $S(v)=\begin {bmatrix} 0 &-z &y \\ z & 0 &-x \\ -y & x &0 \end{bmatrix}$ and $x,y,z$ are coordinates of unit vector representing axis.
In your case $v=[1/3 \ \ \ 2/3 \ \ \ 2/3]^T$.
For angle $\pi/2$ the formula has form
$R(v,\theta)=I+ S(v)+ S^2(v)$.