Convert Euler-Rodrigues vector to rotation angles
Utilities / Axes Transformations
The Rodrigues to Rotation Angles block converts the 3-element Euler-Rodrigues vector into rotation angles.
rod— Euler-Rodrigues vector
Euler-Rodrigues vector determined from rotation angles.
R1,R2,R3— Rotation angles
Rotation angles, in radians, from which to determine the Euler-Rodrigues vector. Quaternion scalar is the first element.
Rotation order— Rotation order
Rotation order for three wind rotation angles.
For the 'ZYX', 'ZXY', 'YXZ', 'YZX', 'XYZ', and 'XZY' rotations, the block generates an R2 angle that lies between ±pi/2 radians (±90 degrees), and R1 and R3 angles that lie between ±pi radians (±180 degrees).
For the 'ZYZ', 'ZXZ', 'YXY', 'YZY', 'XYX', and 'XZX' rotations, the block generates an R2 angle that lies between 0 and pi radians (180 degrees), and R1 and R3 angles that lie between ±pi (±180 degrees). However, in the latter case, when R2 is 0, R3 is set to 0 radians.
An Euler-Rodrigues vector represents a rotation by integrating a direction cosine of a rotation axis with the tangent of half the rotation angle as follows:
are the Rodrigues parameters. Vector represents a unit vector around which the rotation is performed. Due to the tangent, the rotation vector is indeterminate when the rotation angle equals ±pi radians or ±180 deg. Values can be negative or positive.
 Dai, J.S. "Euler-Rodrigues formula variations, quaternion conjugation and intrinsic connections." Mechanism and Machine Theory, 92, 144-152. Elsevier, 2015.