De Moivre's formula for dual quaternions

Kabadayi H., YAYLI Y.

Kuwait Journal of Science and Engineering, cilt.38, sa.1 A, ss.15-23, 2011 (SCI-Expanded) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 38 Sayı: 1 A
  • Basım Tarihi: 2011
  • Dergi Adı: Kuwait Journal of Science and Engineering
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.15-23
  • Anahtar Kelimeler: De moivre, Dual quaternion, Euler, Screw motion
  • Ankara Üniversitesi Adresli: Evet

Özet

By E. Cho (1998), Euler's formula and De Moivre's formula are given for real quaternions and existence of uncountably many unit quaternions satisfying x n = 1 for n ≥ 3 is shown. In this paper, first of all geometrical interpretation of unit dual quaternions is given and unit dual quaternions are shown to work as screw operators, and group structures of these are given. Moreover, De Moivre's formula and Euler's formula for dual quaternions are obtained. Lastly, solutions of the equation x n = 1 is discussed and while the equation x n = 1 has uncountably many solutions for real quaternions, it is shown not to have solutions for a general unit dual quaternion.