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Convert Euler-Rodrigues vector to rotation angles

**Library:**Aerospace Blockset / Utilities / Axes Transformations

The Rodrigues to Rotation Angles block converts the three-element Euler-Rodrigues vector into rotation angles. The rotation used in this block is a passive transformation between two coordinate systems. For more information on Euler-Rodrigues vectors, see 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:

$$\begin{array}{l}{b}_{x}=\mathrm{tan}\left(\frac{1}{2}\theta \right){s}_{x},\\ {b}_{y}=\mathrm{tan}\left(\frac{1}{2}\theta \right){s}_{y},\\ {b}_{z}=\mathrm{tan}\left(\frac{1}{2}\theta \right){s}_{z}\end{array}$$

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.

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

Direction Cosine Matrix to Rodrigues | Rodrigues to Direction Cosine Matrix | Rodrigues to Quaternions | Quaternions to Rodrigues | Rotation Angles to Rodrigues