Rodrigues to Direction Cosine Matrix
Convert Euler-Rodrigues vector to direction cosine matrix
Aerospace Blockset / Utilities / Axes Transformations
The Rodrigues to Direction Cosine Matrix block determines the 3-by-3 direction cosine matrix from a three-element Euler-Rodrigues vector. 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 from which to determine the direction cosine matrix.
DCM — Direction cosine matrix
Direction cosine matrix determined from the Euler-Rodrigues 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.