Rotation Matrix

Rotation Matrix with inputs angle in rad and rotation axis.

Property	Value
Result	Tensor-valued function
Data Types	Tensor2

There are 3 possible cases:

rotation_matrix(phi,3)

\(\begin{equation} \mathbf{R} = \begin{bmatrix} \cos \varphi & -\sin \varphi & 0 \\ \sin \varphi & \cos \varphi & 0 \\ 0 & 0 & 1 \end{bmatrix} \end{equation}\)

rotation_matrix(phi,2)

\(\begin{equation} \mathbf{R} = \begin{bmatrix} \cos \varphi & 0 & \sin \varphi\\ 0 & 1 & 0 \\ -\sin \varphi & 0 & \cos \varphi\\ \end{bmatrix} \end{equation}\)

rotation_matrix(phi,1)

\(\begin{equation} \mathbf{R} = \begin{bmatrix} 1 & 0 & 0 \\ 0 &\cos \varphi & -\sin \varphi\\ 0 & \sin \varphi & \cos \varphi\\ \end{bmatrix} \end{equation}\)

Example

real(kind=8) :: phi
type(Tensor2)  :: R

R = rotation_matrix(phi,1)