The Application of Euler-Rodrigues Formula over Hyper-Dual Matrices

Abstract

The Lie group over the hyper-dual matrices and its corresponding Lie algebra are first introduced in this study. One of Euler's strategies called the Euler-Rodrigues formula is applied to the matrices of hyper-dual rotations. The fundamental relationship between the hyper-dual numbers and the dual numbers allows us to apply the formula on dual lines and two intersecting real lines in the three-dimensional dual and Euclidean spaces, respectively.