What is the Rotation Tensor Matrix for Rotation About e1+e2 Axis?

[samee]

Homework Statement

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

Homework Equations

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

cosθ -sinθ 0
sinθ cosθ 0
0 0 0

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?

 

[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 ?

 

[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 ^_^

 

[tiny-tim]

0 1 0
1 0 0
0 0 1

erm …

the determinant of that is -1 ​