Dual Quaternion Functions and Its Applications

Abstract

A dual quaternion is associated with two quaternions that have basis elements $e_0$, $e_1$, $e_2$, $e_3$, and $\epsilon$. Dual numbers are often written in the form $z=\zeta +\epsilon {\zeta }^{*}$, where $\epsilon$ is the dual identity and has the properties ${\epsilon }^2=0(\epsilon \ne 0)$. We research the properties of some regular functions with values in dual quaternion and give applications of the extension problem for dual quaternion functions.