Kinematic Applications of Hyper-Dual Numbers

Aslan S.

INTERNATIONAL ELECTRONIC JOURNAL OF GEOMETRY, vol.14, no.2, pp.292-304, 2021 (ESCI) identifier identifier

  • Publication Type: Article / Article
  • Volume: 14 Issue: 2
  • Publication Date: 2021
  • Doi Number: 10.36890/iejg.888373
  • Journal Name: INTERNATIONAL ELECTRONIC JOURNAL OF GEOMETRY
  • Journal Indexes: Emerging Sources Citation Index (ESCI), Scopus, TR DİZİN (ULAKBİM)
  • Page Numbers: pp.292-304
  • Keywords: Dual numbers, E. Study mapping, hyper-dual numbers, hyper-dual angle
  • Ankara University Affiliated: Yes

Abstract

Hyper-dual numbers are a new number system that is an extension of dual numbers. A hyperdual number can be written uniquely as an ordered pair of dual numbers. In this paper, some basic algebraic properties of hyper-dual numbers are given using their ordered pair representaions of dual numbers. Moreover, the geometric interpretation of a unit hyper-dual vector is given in module as a dual line. And a geometric interpretation of a subset of unit hyper-dual sphere (the set of all unit hyper-dual vectors) is given as two intersecting perpendicular lines in 3-dimensional real vector space.