# Matrix of a Rotation Tensor

1. Mar 2, 2012

### samee

1. The problem statement, all variables and given/known data

Write the matrix of a rotation tensor corresponding to the rotation by angle θ about an axis aligned with e1+e2

2. Relevant equations

I know that the matrix for a rotation tensor about e3 is;

cosθ -sinθ 0
sinθ cosθ 0
0 0 0

3. The attempt at a solution

I assume that the rotation would be changing only on the e3 axis because the axis are aligned with e1+e2, right? So the matrix will be all zero with the R33 component being some complicated rotated value?

Last edited: Mar 2, 2012
2. Mar 2, 2012

### tiny-tim

hi samee!

(try using the X2 button just above the Reply box )

how about rotating e1+e2 onto e1, then rotating through θ, then rotating e1 back again onto e1 +e2 ?

3. Mar 2, 2012

### samee

Okay! I had some new revelations.

I know that (R-I)u=0 where R is the rotation tensor, I is Identity and u is some vector, here it's e1+e3.

So, this equation will be true if the R matrix is;

0 1 0
1 0 0
0 0 1

BUT!!!! I think it needs to be in sinθ and cosθ instead of 1.... right?

Also- thanks for the tip on the X2 ^_^

4. Mar 2, 2012

### tiny-tim

erm

the determinant of that is -1