Rodrigues’ rotation formula

Rodrigues’ rotation formula gives a convenient way to write the general rotation matrix in $R^{3}$ .

If $[v_{1},v_{2},v_{3}]$ is a unit vector on the rotation axis, and $\theta$ is the rotation angle about that axis, then the rotation matrix is given by

I+\sin(\theta)A+(1-\cos(\theta))A^{2}

where $I$ is the identity matrix and

A=\begin{pmatrix}0&-v_{3}&v_{2}\\ v_{3}&0&-v_{1}\\ -v_{2}&v_{1}&0\end{pmatrix}

Title	Rodrigues’ rotation formula
Canonical name	RodriguesRotationFormula
Date of creation	2013-03-22 15:20:04
Last modified on	2013-03-22 15:20:04
Owner	acastaldo (8031)
Last modified by	acastaldo (8031)
Numerical id	7
Author	acastaldo (8031)
Entry type	Result
Classification	msc 51-00
Classification	msc 15-00
Related topic	DecompositionOfOrthogonalOperatorsAsRotationsAndReflections