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m Conversion between Quaternions and Euler angles moved to Conversion between quaternions and Euler angles |
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:<math>\mathbf{q}_2 = \sin(\alpha/2)\cos(\beta_y)</math>
:<math>\mathbf{q}_3 = \sin(\alpha/2)\cos(\beta_z)</math>
where <math>\alpha</math> is a simple rotation angle and <math>\beta_x</math>, <math>\beta_y</math>, <math>\beta_z, </math> are the "[[unit vector|direction cosine]]s" locating the axis of rotation (Euler's Theorem).
Similarly for Euler angles, we use (in terms of [[flight dynamics]]):
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