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Line 3: ==Definition== There are [[Quaternions_and_spatial_rotation#Alternative_conventions\|two representations]] of quaternions. This article uses the more popular Hamilton. 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_w & q_x & q_y & q_z \end{bmatrix}^T</math>~~ A quaternion has 4 scaler values: {{mvar\|q<sub>w</sub>}} (the real part) and {{mvar\|q<sub>x</sub> q<sub>y</sub> q<sub>z</sub>}} (the imaginary part). A unit [[quaternion]] can be described as: :<math>\|\mathbf{q}\|^2 = q_w^2 + q_x^2 + q_y^2 + q_z^2 = 1</math>

Conversion between quaternions and Euler angles: Difference between revisions