Conversion between quaternions and Euler angles: Difference between revisions

Revision as of 06:24, 17 August 2005

Revision as of 07:15, 17 August 2005

Line 9:

:<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).

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

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

* Roll - <math>\phi</math>: rotation about the X-axis