Modified Gibbs's representation of rotation matrix
S. I. Kruglov, V. Barzda
TL;DR
This paper introduces a modified Gibbs's rotation matrix, linking it with Euler angles, quaternions, and Cayley-Klein parameters, and derives composition laws for rotations, enhancing understanding of rotation representations.
Contribution
It presents a new modified Gibbs's rotation matrix and establishes its connections with various rotation parameterizations, including Rodrigues and Gibbs, along with composition laws for quaternions.
Findings
Derived a modified Gibbs's rotation matrix.
Connected Gibbs's matrix with Euler angles, quaternions, Cayley-Klein parameters.
Provided a composition law for quaternion-based rotations.
Abstract
A modified Gibbs's rotation matrix is derived and the connection with the Euler angles, quaternions, and CayleyKlein parameters is established. As particular cases, the Rodrigues and Gibbs parameterizations of the rotation are obtained. The composition law of two rotations from the quaternion representation is presented showing a convenient expression for calculating the successive rotations.
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Taxonomy
TopicsAdvanced Mathematical Theories and Applications · Mathematics and Applications · Matrix Theory and Algorithms