# FEA - Rotation Matrix of Angular Deflection

1. Apr 13, 2012

### huyrich

I am trying to use FEA with space frame element. I know that for rotating an angle a around the z-axis, the translational displacements of the local and global coordinates are related through the rotation matrix:

$$\begin{bmatrix}cos(a) & sin(a) & 0 \\ -sin(a) & cos(a) & 0 \\ 0 & 0 & 1\end{bmatrix}$$

But how about angular displacement (deflection), I thought the rotation matrix for them would be:

$$\begin{bmatrix}1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1\end{bmatrix}$$

But it turns out it is the same with the first rotation matrix (or is it not?). Can anyone give me some hints how to derive or verify this?