Eric Lengyel: Created page with "NOTOC A ''rotation'' is a proper isometry of Euclidean space performed by the operator :$$\mathbf R = \boldsymbol l\sin\dfrac{\phi}{2} + {\large\unicode{x1d7d9}}\cos\dfrac{\phi}{2}$$ , where $$\boldsymbol l$$ is a unitized line corresponding to the axis of rotation. This operator is identical to the [http://rigidgeometricalgebra.org/wiki/index.php?title=Rotation rotation operator in rigid geometric algebra] but with the extra factor of $$\mathbf e_5$$. It rotat..."

2023-08-06T03:19:49Z

Created page with "__NOTOC__ A ''rotation'' is a proper isometry of Euclidean space performed by the operator :$$\mathbf R = \boldsymbol l\sin\dfrac{\phi}{2} + {\large\unicode{x1d7d9}}\cos\dfrac{\phi}{2}$$ , where $$\boldsymbol l$$ is a unitized line corresponding to the axis of rotation. This operator is identical to the [http://rigidgeometricalgebra.org/wiki/index.php?title=Rotation rotation operator in rigid geometric algebra] but with the extra factor of $$\mathbf e_5$$. It rotat..."

New page

__NOTOC__
A ''rotation'' is a proper isometry of Euclidean space performed by the operator

:$$\mathbf R = \boldsymbol l\sin\dfrac{\phi}{2} + {\large\unicode{x1d7d9}}\cos\dfrac{\phi}{2}$$ ,

where $$\boldsymbol l$$ is a unitized [[line]] corresponding to the axis of rotation. This operator is identical to the [http://rigidgeometricalgebra.org/wiki/index.php?title=Rotation rotation operator in rigid geometric algebra] but with the extra factor of $$\mathbf e_5$$. It rotates an object $$\mathbf x$$ through the angle $$\phi$$ about the line $$\boldsymbol l$$ when used with the sandwich antiproduct $$\mathbf R \mathbin{\unicode{x27C7}} \mathbf x \mathbin{\unicode{x27C7}} \smash{\mathbf{\underset{\Large\unicode{x7E}}{R}}}$$.

== See Also ==

* [[Translation]]

Rotation - Revision history