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.

2.1 Cartesian and polar coordinates A vector or a position (the tip of the vector) in a two-dimensional space can be given either in cartesian coordinates (x,y) or in polar coordinates (r,f), relative to a frame of reference: f r y x The formulas for transforming one representation to another are: x = r cosf y = r sinf r = q x2 +y2 f = tan 1 y x.

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  Glean, Coordinates, Tutorials, Euler, Polar, Quaternion, Polar coordinates, Tutorial on euler angles and quaternions

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