Dual Quaternions and Dual Quaternionic Curves - Dagdeviren, Ali; Yuce, Salim (UNIV NIS, FAC SCI MATH, 2019)
After a brief review of the different types of quaternions, we develop a new perspective for dual quaternions with dividing two parts. Due to this new perspective, we will define the isotropic and non-isotropic dual quaternions. Then we will also give the basic algebraic concepts about the dual quaternions. Moreover, we define isotropic dual quaternionic curves and non-isotropic dual quaternionic curves. Via these definitions we find Serret-Frenet formulae for isotropic dual quaternionic curves. Finally, we will use these results to derive the Serret-Frenet formulae for non-isotropic dual quaternionic curves.
Keywords: Dual Quaternions; Dual Quaternionic Curves; Serret-Frenet Frame; Mathematics