Rodrigues to Rotation Angles
Convert Euler-Rodrigues vector to rotation angles
Aerospace Blockset / Utilities / Axes Transformations
The Rodrigues to Rotation Angles block converts the three-element Euler-Rodrigues vector into rotation angles. The rotation used in this block is a passive transformation between two coordinate systems. For more information on Euler-Rodrigues vectors, see Algorithms.
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
ZYX (default) |
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.
|Type: character vector|
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.