On HD-Split Euler-Rodrigues Equations

Abstract

In this work, we introduce HD-split Euler-Rodrigues equations. First, we include the basic concepts of dual numbers, dual vectors, HD-numbers, HD-vectors and HD-split vectors, which form the basis of the study. Then we obtain HD-split Euler-Rodrigues relations for HD-unit spacelike axes and HD-unit timelike axes. Thanks to these relations, we obtain HD-split rotation matrices and we examine the relationships with the E.Study transformation defined for HD-split vectors. We also reconstruct Euler's fixed point theorem with HD-split rotation matrices. Finally, we provide extensive and interesting examples that support the theory.