8.1 Description

$\mathrm{SO}(3)$ is the group of rotations in 3D space, represented by orthogonal matrices with unit determinant. It has three degrees of freedom: one for each differential rotation axis. The inverse is given by the transpose:

$\displaystyle \mathbf{R}$	$\displaystyle \in$	$\displaystyle \mathrm{SO}(3)\subset\mathbb{R}^{3\times3}$	(92)
$\displaystyle \mathbf{R}^{-1}$	$\displaystyle =$	$\displaystyle \mathbf{R}^{T}$	(93)
$\displaystyle \det\left(\mathbf{R}\right)$	$\displaystyle =$	$\displaystyle 1$	(94)

Ethan Eade 2012-02-16