QUATERNIONS AND HOMOTHETIC MOTIONS IN EUCLIDEAN AND LORENTZIAN SPACES

Yuca G., Yayli Y.

HONAM MATHEMATICAL JOURNAL, cilt.45, sa.2, ss.198-214, 2023 (ESCI) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 45 Sayı: 2
  • Basım Tarihi: 2023
  • Doi Numarası: 10.5831/hmj.2023.45.2.198
  • Dergi Adı: HONAM MATHEMATICAL JOURNAL
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI)
  • Sayfa Sayıları: ss.198-214
  • Anahtar Kelimeler: Homothetic motion, Hamilton operator, quaternion, Lorentzian space, dual space, kinematics, SURFACES
  • Ankara Üniversitesi Adresli: Evet

Özet

In the present paper, we investigate homothetic motions de-termined by quaternions, which is a general form of our previous paper [20]. We introduce a transition between homothetic motions in 3D and 4D Euclidean and Lorentzian spaces. In other words, we give a new method that works as a handy tool for obtaining Lorentzian homothetic motions from Euclidean homothetic motions. Moreover, some remarkable prop-erties of homothetic motions, which are given in former studies on this subject, are also examined by dual transformations. Then, we present applications and visualize them with 3D-plots. Finally, we investigate homothetic motions in dual spaces because of the importance in many fields related to kinematics.