Split quaternions and rotations in semi euclidean space E-2(4)

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Kula L., Yayli Y.

JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY, cilt.44, sa.6, ss.1313-1327, 2007 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 44 Sayı: 6
  • Basım Tarihi: 2007
  • Doi Numarası: 10.4134/jkms.2007.44.6.1313
  • Dergi Adı: JOURNAL OF THE KOREAN MATHEMATICAL SOCIETY
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1313-1327
  • Anahtar Kelimeler: hyperbolic number, split quaternion, generalized inverse, rotation, timelike plane of index 1, timelike plane of index 2, spacelike plane
  • Ankara Üniversitesi Adresli: Evet

Özet

We review the algebraic structure of H' and show that H' has a scalar product that allows as to identify it with semi Euclidean E-2(4) We show that a pair q and p of unit split quaternions in H' determines a rotation R-qp : H' <-> H'. Moreover, we prove that R-qp is a product of rotations in a pair of orthogonal planes in E-2(4). To do that we call upon one tool from the theory of second ordinary differential equations.