Some variations of dual Euler-Rodrigues formula with an application to point-line geometry

Kahveci D., GÖK İ., YAYLI Y.

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, sa.2, ss.1029-1039, 2018 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Basım Tarihi: 2018
  • Doi Numarası: 10.1016/j.jmaa.2017.11.020
  • Dergi Adı: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.1029-1039
  • Anahtar Kelimeler: Dual Euler-Rodrigues formula, Dual Lie groups, Dual Lie algebra, Point-line geometry, Screw motion, Dual quaternions, SPLIT QUATERNIONS, MOTION
  • Ankara Üniversitesi Adresli: Evet

Özet

This paper examines the Euler Rodrigues formula in dual 3-space D-3 by analyzing its variations such as vectorial form, exponential map, point-line theory and quaternions which have some intrinsic relations. Contrary to the Euclidean case, dual rotation in dual 3-space corresponds to a screw motion in Euclidean 3-space. This paper begins by explaining dual motion in terms of the given dual axis and angle. It will then go on to express dual Euler-Rodrigues formula with algebraic methods. Furthermore, an application of dual Euler-Rodrigues formula to point-line geometry is accomplished and point line displacement operator is obtained by dual Euler Rodrigues formula. Finally, dual Euler Rodrigues formula is presented with the help of dual Euler-Rodrigues parameters that is expressed as a dual quaternion. (C) 2017 Elsevier Inc. All rights reserved.