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quat2rod

Convert quaternion to Euler-Rodrigues vector

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Syntax

rod=quat2rod(quat)

Description

rod=quat2rod(quat) function calculates the Euler-Rodrigues vector, rod, for a given quaternion quat. The quaternion input and resulting Euler-Rodrigues vector represent a right-hand passive transformation from frame A to frame B.

Aerospace Toolbox uses quaternions that are defined using the scalar-first convention. This function normalizes all quaternion inputs.

example

Examples

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Open Live Script

This example shows how to determine the Euler-Rodrigues vector from the quaternion.

q = [-0.7071 0 0.7071 0]
q = 1×4

   -0.7071         0    0.7071         0


r = quat2rod( q )
r = 1×3

         0   -1.0000         0

Input Arguments

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M-by-4 array of quaternions. quat has its scalar number as the first column.

Data Types: double

Output Arguments

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M-by-3 matrix containing M Euler-Rodrigues vectors.

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.

Version History

Introduced in R2017a

See Also

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