Rodrigues to Direction Cosine Matrix

Convert Euler-Rodrigues vector to direction cosine matrix

• Library:

• Aerospace Blockset / Utilities / Axes Transformations

• 

Description

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.

Ports

Input

rod — Euler-Rodrigues vector

three-element vector

Euler-Rodrigues vector from which to determine the direction cosine matrix.

Data Types: double

Output

DCM — Direction cosine matrix

3-by-3 matrix

Direction cosine matrix determined from the Euler-Rodrigues vector.

Data Types: double

Algorithms

An Euler-Rodrigues vector $$\stackrel{\rightharpoonup }{b}$$ represents a rotation by integrating a direction cosine of a rotation axis with the tangent of half the rotation angle as follows:

$$\overrightarrow{b}=\left[\begin{array}{ccc}{b}_x& b_y& b_z\end{array}\right]$$

where:

$$\begin{array}{l}{b}_x=\tan \left(\frac{1}{2}\theta \right)s_x,\\ b_y=\tan \left(\frac{1}{2}\theta \right)s_y,\\ b_z=\tan \left(\frac{1}{2}\theta \right)s_z\end{array}$$

are the Rodrigues parameters. Vector $$\stackrel{\rightharpoonup }{s}$$ 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.

Extended Capabilities

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

Version History

Introduced in R2017a