Rotation Angles to Rodrigues
Convert rotation angles to Euler-Rodrigues vector
Libraries:
Aerospace Blockset /
Utilities /
Axes Transformations
Description
The Rotation Angles to Rodrigues block converts the rotation described by the three rotation
angles R1,R2,R3
into the 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
Output
Parameters
Algorithms
An Euler-Rodrigues vector represents a rotation by integrating a direction cosine of a rotation axis with the tangent of half the rotation angle as follows:
where:
are the Rodrigues parameters. Vector 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
Version History
Introduced in R2017a