# 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 RodriguesRotationFormula 2013-03-22 15:20:04 2013-03-22 15:20:04 acastaldo (8031) acastaldo (8031) 7 acastaldo (8031) Result msc 51-00 msc 15-00 DecompositionOfOrthogonalOperatorsAsRotationsAndReflections