Conversion between quaternions and Euler angles: Difference between revisions

Revision as of 23:50, 17 July 2006

Revision as of 02:46, 18 September 2006

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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>α is a simple rotation angle and and cos(β<mathsub>\beta_x''x''</mathsub>), cos(β<mathsub>\beta_y''y''</mathsub>,) and cos(β<mathsub>\beta_z, ''z''</mathsub>) are the "[[unit vector|direction
cosine]]s" locating the axis of rotation (Euler's Theorem).

[[Image:Flight_dynamics.jpg|right|thumb]]

Similarly for Euler angles, we use (in terms of [[flight dynamics]]):