MAE142_Lecture8

# MAE142_Lecture8 - Euler Parameters and Quaternions...

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Euler Parameters and Quaternions Quaternion Definition L2B Transformation Euler/Quaternion Conversions MAE 142 NASA Image

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2 MAE 142 Quaternion Definition Euler's Principal Rotation Theorem states that a completely general re-orientation of a rigid body can be accomplished by a single rotation about some fixed axis. [ b 0 b x b y b z ] = [ cos / 2 B x sin 2 B y sin 2 B z sin 2 ] = Euler principal angle b = [ B x B y B z ] = unit length principal vector Four Euler Parameters , also known as Quaternions Euler's principal axis and angle can be computed once four quaternions are known. = 2cos 1 b 0 b = 1 sin 2 [ b x b y b z ]
3 MAE 142 Normalization A constraint equation exists because there are four Euler parameters to define a three-dimensional orientation. b 0 2 b x 2 b y 2 b z 2 = cos 2 / 2  B x 2 B y 2 B z 2 sin 2 2 B x 2 B y 2 B z 2 = 1 cos 2 2  sin 2 2 = 1 b 0 2 b x 2 b y 2 b z 2 = 1 But and

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4 MAE 142
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MAE142_Lecture8 - Euler Parameters and Quaternions...

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