Quaternions to Rodrigues
Convert quaternion to Euler-Rodrigues vector
Aerospace Blockset / Utilities / Axes Transformations
The Quaternions to Rodrigues block converts the 4-by-1 quaternion to the three-element Euler-Rodrigues vector. Aerospace Blockset™ uses quaternions that are defined using the scalar-first convention. This block normalizes all quaternion inputs. The rotation used in this function is a passive transformation between two coordinate systems. For more information on Euler-Rodrigues vectors, see Algorithms.
Quaternion — Quaternion
Quaternion from which to determine Euler-Rodrigues vector. Quaternion scalar is the first element.
rod — Euler-Rodrigues vector
Euler-Rodrigues vector determined from the quaternion.
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.