rod2quat
Convert Euler-Rodrigues vector to quaternion
Syntax
Description
function
calculates the quaternion, quat
=rod2quat(R
)quat
, for a given Euler-Rodrigues
(also known as Rodrigues) vector, R
. The Euler-Rodrigues vector
input and resulting quaternion represent a right-hand passive transformation from
frame A to frame B.
Aerospace Toolbox uses quaternions that are defined using the scalar-first convention.
Examples
Input Arguments
Output Arguments
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.
Version History
Introduced in R2017a