MATLAB: Aerospace toolbox rotations: right-handed or left-handed

Aerospace Toolboxrotations

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?

Best Answer

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
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