Conversion between quaternions and Euler angles: Difference between revisions

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==Definition==

There are two representations of quaternions. Hamilton (where w is the first component) and [[JPL]] (where w is the last component).<ref>W. G. Breckenridge, "Quaternions proposed standard conventions," NASA Jet Propulsion Laboratory, Technical Report, Oct. 1979.</ref>. This article uses Hamilton for some formulas. A unit [[quaternion]] can be described as:

:<math>\mathbf{q} = \begin{bmatrix} q_0 & q_1 & q_2 & q_3 \end{bmatrix}^T = \begin{bmatrix} q_w & q_x & q_y & q_z \end{bmatrix}^T</math>

:<math>|\mathbf{q}|^2 = q_0^2 + q_1^2 + q_2^2 + q_3^2 = q_w^2 + q_x^2 + q_y^2 + q_z^2 = 1</math>