Transcription of A Tutorial on Euler Angles and Quaternions
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A Tutorial on Euler Angles and Quaternions
A Tutorial on Euler Angles and QuaternionsMoti Ben-AriDepartment of Science TeachingWeizmann Institute of 2014 17 by Moti work is licensed under the Creative Commons Attribution-ShareAlike UnportedLicense. To view a copy of this license, send a letter to Creative Commons, 444 Castro Street, Suite 900, MountainView, California, 94041, 1 IntroductionYou sitting in an airplane at night, watching a movie displayed on the screen attachedto the seat in front of you. The airplane gently banks to the left. You may feel the slightacceleration, but you won t see any change in the position of the movie screen. Both youand the screen are in the sameframe of reference, so unless you stand up or make anothermove, the position and orientation of the screen relative to your position and orientationwon t change.
Construct two right triangles: (1) Drop the perpendicular from A0to the x-axis to form the right triangle 4OA0C; (b) Construct a line through A0parallel to the x-axis and a line through B0parallel to the y-axis. They intersect at C0to form the right triangle 4B0A0C0. Since A0C0is parallel to CO, 6C0A0O = 6A0OC = q. 6OA0B0is a right angle and ...
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