Reference documentation for deal.II version 8.5.0
Physics::Transformations::Rotations Namespace Reference

## Functions

Rotation matrices
template<typename Number >
Tensor< 2, 2, Number > rotation_matrix_2d (const Number &angle)

template<typename Number >
Tensor< 2, 3, Number > rotation_matrix_3d (const Point< 3, Number > &axis, const Number &angle)

## Detailed Description

Transformation functions and tensors that are defined in terms of rotation angles and axes of rotation.

## Function Documentation

template<typename Number >
 Tensor<2,2,Number> Physics::Transformations::Rotations::rotation_matrix_2d ( const Number & angle )

Returns the rotation matrix for 2-d Euclidean space, namely

$\mathbf{R} := \left[ \begin{array}{cc} cos(\theta) & sin(\theta) \\ -sin(\theta) & cos(\theta) \end{array}\right]$

where $$\theta$$ is the rotation angle given in radians. In particular, this describes the counter-clockwise rotation of a vector relative to a fixed set of right-handed axes.

Parameters
$\mathbf{R} := cos(\theta)\mathbf{I} + sin(\theta)\mathbf{W} + (1-cos(\theta))\mathbf{u}\otimes\mathbf{u}$
where $$\mathbf{u}$$ is the axial vector (an axial vector) and $$\theta$$ is the rotation angle given in radians, $$\mathbf{I}$$ is the identity tensor and $$\mathbf{W}$$ is the skew symmetric tensor of $$\mathbf{u}$$.