PlanetMath: Rodrigues' rotation formula

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Rodrigues' rotation formula

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Rodrigues' rotation formula gives a convenient way to write the general rotation matrix in .

If is a unit vector on the rotation axis, and $\theta$ is the rotation angle about that axis, then the rotation matrix is given by

$\displaystyle I + \sin(\theta) A +(1-\cos(\theta))A^2$

where is the identity matrix and

$\displaystyle A = \begin{pmatrix} 0 & -v_3 & v_2 \ v_3 & 0 & -v_1 \ -v_2 & v_1 & 0 \end{pmatrix}$

"Rodrigues' rotation formula" is owned by acastaldo.

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Cross-references: identity matrix, angle, axis, rotation, unit vector, rotation matrix
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This is version 4 of Rodrigues' rotation formula, born on 2005-06-13, modified 2005-06-13.
Object id is 7150, canonical name is RodriguesRotationFormula.
Accessed 4268 times total.

Classification:

AMS MSC:	15-00 (Linear and multilinear algebra; matrix theory :: General reference works )
	51-00 (Geometry :: General reference works )

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