Rotation¶

Type:	Rotation
Range:	[SO(3)]
Default:	-/-
Appearance:	simple

The rotation parameter together with the translation parameter Translation is used to apply an affine coordinate transformation to the tensor field imported from the JCM-fieldbag.

A JCM-fieldbag is equipped with an internal coordinate system as it was used when creating the fieldbag. The tensor fields contained therein refer to this internal coordinate system.

To transform the “thermal conductivity “-tensor field $\VField{k}_\mathrm{fieldbag}$ contained in the JCM-fieldbag to the currently used coordinate system a rotation matrix $\TField{R} \in \mathrm{SO}(3)$ and a translation vector $\pvec{x}_0$ are applied as follows:

$\begin{eqnarray*} \VField{k} (\pvec{x}) & = & \void{\TField{R}} {\VField{k}_{\mathrm{fieldbag}}} \transpose{\TField{R}} \left( \TField{R}^{-1} ( \pvec{x}-\pvec{x_0} ) \right) \end{eqnarray*}$

The corresponding syntax is:

FieldBag {
  ...
  Rotation = ... # sets rotation matrix R
  Translation = ... # sets translation vector t
  ...
}