Documentation

Quaternions to Rodrigues

Convert quaternion to Euler-Rodrigues vector

  • Library:
  • Utilities / Axes Transformations

Description

The Quaternions to Rodrigues block converts the 4-by-1 quaternion to the 3-element Euler-Rodrigues vector.

Ports

Input

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

Data Types: double

Output

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Euler-Rodrigues vector determined from the quaternion.

Data Types: double

Algorithms

  • 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:

    b=[bxbybz]

    where:

    bx=tan(12θ)sx,by=tan(12θ)sy,bz=tan(12θ)sz

    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.

References

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

Introduced in R2017a

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