Conversion between quaternions and Euler angles: Difference between revisions

Revision as of 06:44, 14 February 2025

Revision as of 06:51, 14 February 2025

Line 300:

:<math>

\begin{align}

\mathbf{v}^\prime & = \mathbf{q v q^\ast} = (0, (q_w^2 - \vec{q}\cdot\vec{q})\vec{v} + 2 q_w \vec{q} \times \vec{v} +

2\vec{q}\times (\vec{q}\times\vec{v} )) \\

\end{align}

Line 306:

which upon defining <math>\vec{t} = 2\vec{q} \times \vec{v}</math> can be written in terms of scalar and vector parts as

:<math>

(0, \vec{v}^{\,\prime}) = (0, (q_w^2 - \vec{q}\cdot\vec{q})\vec{v} + q_w \vec{t} + \vec{q} \times \vec{t} ).

</math>