Using Rotations to Build Aerospace Coordinate Systems - Defence ...
Using Rotations to Build Aerospace Coordinate Systems - Defence ...
Using Rotations to Build Aerospace Coordinate Systems - Defence ...
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DSTO–TN–0640<strong>Using</strong> QuaternionsThe necessary quaternions areQ x =Q y =()cos 45 ◦ , sin45 ◦ (1, 0, 0) = √ 1 (1, 1, 0, 0), 2()cos 45 ◦ , sin45 ◦ (0, 1, 0) = √ 1 (1, 0, 1, 0). 2(A4)The combined quaternion rotation is Q y Q x :Q y Q x = 1 2 (1, 0, 1, 0)(1, 1, 0, 0) = 1 (1, 1, 1, −1)(2√ ) ()1 3=2 , (1, 1, −1)√ = cos 60 ◦ (1, 1, −1), √ sin60 ◦ , (A5)2 3 3which is a rotation of 120 ◦ around (1, 1, −1)/ √ 3, just as we found in (A3).22
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