Conversion between quaternions and Euler angles: Difference between revisions

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Reverted my own change. I misunderstood the meaning of alpha.
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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 α is a simple rotation angle (the value in radians of the angle of rotation) and cos(β<sub>''x''</sub>), cos(β<sub>''y''</sub>) and cos(β<sub>''z''</sub>) are the "[[EulerUnit vector|direction Anglescosines]]" locating the axis of rotation (Euler's Theorem).
 
===Relationship with Tait-Bryan angles===