INVOLUTIONS IN SEMI-QUATERNIONS

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Bekar M., YAYLI Y.

JOURNAL OF GEOMETRY AND SYMMETRY IN PHYSICS, cilt.41, ss.1-16, 2016 (ESCI) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 41
  • Basım Tarihi: 2016
  • Doi Numarası: 10.7546/jgsp-41-2016-1-16
  • Dergi Adı: JOURNAL OF GEOMETRY AND SYMMETRY IN PHYSICS
  • Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus
  • Sayfa Sayıları: ss.1-16
  • Anahtar Kelimeler: Dual-quaternions, involutions, planar-motion, semi-quaternions
  • Ankara Üniversitesi Adresli: Evet

Özet

Involutions are self-inverse and homomorphic linear mappings. Rotations, reflections and rigid-body (screw) motions in three-dimensional Euclidean space R-3 can be represented by involution mappings obtained by quaternions. For example, a reflection of a vector in a plane can be represented by an involution mapping obtained by real-quaternions, while a reflection of a line about a line can be represented by an involution mapping obtained by dual-quaternions. In this paper, we will consider two involution mappings obtained by semi-quternions, and a geometric interpretation of each as a planar-motion in R-3.