Conversion between quaternions and Euler angles: Difference between revisions

Revision as of 06:54, 15 May 2021

Revision as of 17:56, 24 May 2021

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If <math>q_0+iq_1+jq_2+kq_3</math> is not a unit quaternion then the homogeneous form is still a scalar multiple of a rotation matrix, while the inhomogeneous form is in general no longer an orthogonal matrix. This is why in numerical work the homogeneous form is to be preferred if distortion is to be avoided.

The direction cosine matrix (from the rotated Body XYZ coordinates to the original Lab xyz coordinates for a clockwise/lefthand rotation) corresponding to a post-multiply '''Body 3-2-1''' sequence with [[Euler angles]] (ψ, θ, φ) is given by:<ref name=nasa-rotation>{{cite web|last=NASA Mission Planning and Analysis Division|title=Euler Angles, Quaternions, and Transformation Matrices|url=https://ntrs.nasa.gov/archivecitations/nasa/casi.ntrs.nasa.gov/19770024290_1977024290.pdf19770024290|publisher=[[NASA]]|accessdate=1224 January 2013}}{{dead link|date=AprilMay 2021}}</ref>

:<math>

\begin{align}