Documentation

Rotation Angles to Rodrigues

Convert rotation angles to Euler-Rodrigues vector

  • Library:
  • Utilities / Axes Transformations

Description

The Rotation Angles to Rodrigues block converts the rotation described by the three rotation angles R1,R2,R3 into the 3-element Euler-Rodrigues vector.

Ports

Input

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Rotation angles, in radians, from which to determine the Euler-Rodrigues vector. Values must be real.

Data Types: double

Output

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Euler-Rodrigues vector determined from rotation angles.

Data Types: double

Parameters

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Rotation order for three wind rotation angles.

The default limitations for the 'ZYX', 'ZXY', 'YXZ', 'YZX', 'XYZ', and 'XZY' sequences generate an R2 angle that lies between ±pi/2 radians (± 90 degrees), and R1 and R3 angles that lie between ±pi radians (±180 degrees).

The default limitations for the 'ZYZ', 'ZXZ', 'YXY', 'YZY', 'XYX', and 'XZX' sequences generate an R2 angle that lies between 0 and pi radians (180 degrees), and R1 and R3 angles that lie between ±pi (±180 degrees).

Rodrigues transformation is not defined for rotation angles equal to ±pi radians (±180 deg).

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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