Euler–Rodrigues formula variations, quaternion conjugation and intrinsic connections

By J. Dai. 2015

344 citations recorded by the source corpus.

Abstract This paper reviews the Euler–Rodrigues formula in the axis–angle representation of rotations, studies its variations and derivations in different mathematical forms as vectors, quaternions and Lie groups and investigates their intrinsic connections. The Euler–Rodrigues formula in the Taylor series expansion is presented and its use as an exponential map of Lie algebras is discussed particularly with a non-normalized vector. The connection between Euler–Rodrigues parameters and the Euler–Rodrigues formula is then demonstrated through quaternion conjugation and the equivalence between quaternion conjugation and an adjoint action of the Lie group is subsequently presented. The paper provides a rich reference for the Euler–Rodrigues formula, the variations and their connections and for their use in rigid body kinematics, dynamics and computer graphics.

Subfields: Control and Systems Engineering, Ocean Engineering

View Paper: https://www.semanticscholar.org/paper/c388d2b39e769ce7e25138b6abc40144c7a299fb

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Control and Systems Engineering

1. Tao Sun
2. Tian Huang
3. Shuofei Yang
4. J. Dai

In Ocean Engineering

1. Tian Huang
2. Tao Sun
3. Shuofei Yang

Citations in the corpus

• A way of relating instantaneous and finite screws based on the screw triangle product (2017, methodology): “Meanwhile, the consistency between these mappings and the exponential mapping of matrix Lie group/Lie algebra or the Euler-Rodrigues formula was revealed [25-26, 35].”