Mathematics-Online lexicon: Rotation Matrix

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	Mathematics-Online lexicon:
	Rotation Matrix

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A rotation in $\mathbb{R}^3$ with normed rotation axis vector

and rotation angle $\theta$ , which is oriented like a right-handed screw, maps a vector

onto

$\displaystyle Qx = \cos\theta x + (1-\cos\theta) u u^{\operatorname t}x + \sin\theta u \times x \,.$

The corresponding rotation matrix is defined by

$\displaystyle Q: q_{ik}$

$\displaystyle =$

$\displaystyle \cos\theta \;\delta_{ik} + (1-\cos\theta)\;u_iu_k + \sin\theta \sum\limits_j \varepsilon_{ijk}u_j \,,$

with Kornecker symbol $\delta_{ik}$ and $\varepsilon$ -tensor $\varepsilon_{ijk}$ .

(Authors: Höllig/Reble/Höfert)

Example:

automatically generated 3/21/2005