Determine rotation vector from quaternion
The Quaternions to Rotation Angles block converts the
four-element quaternion vector (q0, q1, q2, q3)
into the rotation described by the three rotation angles (R1, R2,
R3). The block generates the conversion by comparing elements in
the direction cosine matrix (DCM) as a function of the rotation angles.
The elements in the DCM are functions of a unit quaternion vector.
For example, for the rotation order
the DCM is defined as:
The DCM defined by a unit quaternion vector is:
From the preceding equation, you can derive the following relationships between DCM elements and individual rotation angles for a ZYX rotation order:
where Ψ is R1, Θ is R2, and Φ is R3.
Specifies the output rotation order for three rotation angles.
From the list, select
XZX. The default is
|4-by-1 quaternion vector||Contains the quaternion vector.|
|3-by-1 vector||Contains the rotation angles, in radians.|
For the 'ZYX', 'ZXY', 'YXZ', 'YZX', 'XYZ', and 'XZY' rotations, the block generates an R2 angle that lies between ±pi/2 radians, and R1 and R3 angles that lie between ±pi radians.
For the 'ZYZ', 'ZXZ', 'YXY', 'YZY', 'XYX', and 'XZX' rotations, the block generates an R2 angle that lies between 0 and pi radians, and R1 and R3 angles that lie between ±pi radians. However, in the latter case, when R2 is 0, R3 is set to 0 radians.