Conversion between quaternions and Euler angles: Difference between revisions

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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 (radians) and <math>\beta_x</math>, <math>\beta_y</math>, <math>\beta_z, </math> are the "direction cosines" oflocating the axis of simple rotation (Euler's Theorem).
 
Similarly for Euler angles, we use: