Aerospace toolbox rotations: right-handed or left-handed?
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I'm getting myself all confused over this. Supposedly, the toolbox uses a right-handed coordinate system ( ref ). But this is producing a left-handed rotation matrix:
>> which angle2dcm
...../Matlab/toolbox/aero/aero/angle2dcm.m
>> angle2dcm(pi/2,0,0,'zyx')
ans =
0.000000000000000 1.000000000000000 0
-1.000000000000000 0.000000000000000 0
0 0 1.000000000000000
This behavior seems relatively consistent throughout the toolbox. Is the documentation just wrong?
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Accepted Answer
Mischa Kim
on 9 Dec 2013
Edited: Mischa Kim
on 9 Dec 2013
It is proper right-handed. The rotation matrix for a right-handed rotation about the z-axis with a rotation angle psi is given by
Rz(psi) = [ cos(psi) sin(psi) 0;
-sin(psi) cos(psi) 0;
0 0 1]
For a rotation angle of 90 deg (pi/2) this results in
angle2dcm(pi/2,0,0,'zyx')
ans =
0.0000 1.0000 0
-1.0000 0.0000 0
0 0 1.0000
As an example, the vetor v in the graph below has coordinates [1; 0; 0] in the un-primed reference frame (left). When rotating the reference frame about 90 deg (right-handed) about the z-axis the vector points in negative y direction, [0; -1: 0], which corresponds to the result from the matrix-vector multiplication:
angle2dcm(pi/2,0,0,'zyx')*[1; 0; 0]
ans =
0.0000
-1.0000
0
4 Comments
Tamas Sarvary
on 24 Jan 2019
@Mischa from the behavior of quatrotate I can see your observation is right but in the documentation that isn't mentioned at all.
"n = quatrotate(q,r) calculates the rotated vector, n, for a quaternion, q, and a vector, r."
James Tursa
on 7 Feb 2020
See also this post. The quatrotate function should probably use the phrase "coordinate system transformation" instead of the phrase "rotated vector".
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