Dual Quaternion Functions and Its Applications

Abstract

A dual quaternion is associated with two quaternions that have basis elements e0, e1, e2, e3, and ε. Dual numbers are often written in the form z=ζ+εζ*, where ε is the dual identity and has the properties ε2=0 (ε≠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.