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Quaternions to Rodrigues

Convert quaternion to Euler-Rodrigues vector

  • Quaternions to Rodrigues block

Aerospace Blockset / Utilities / Axes Transformations


The Quaternions to Rodrigues block converts the 4-by-1 quaternion to the three-element Euler-Rodrigues (Rodrigues) vector. Aerospace Blockset™ uses quaternions that are defined using the scalar-first convention. This block normalizes all quaternion inputs. The quaternion input and the resulting Euler-Rodrigues vector represent a right-hand passive transformation from frame A to frame B. For more information on Euler-Rodrigues vectors, see Algorithms.



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Quaternion from which to determine Euler-Rodrigues vector. Quaternion scalar is the first element.

Data Types: double


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Euler-Rodrigues vector determined from the quaternion.

Data Types: double


  • An Euler-Rodrigues vector b 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 s 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.


[1] Dai, J.S. "Euler-Rodrigues formula variations, quaternion conjugation and intrinsic connections." Mechanism and Machine Theory, 92, 144-152. Elsevier, 2015.

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

Version History

Introduced in R2017a