Applied Mathematics and Mechanics

, Volume 25, Issue 8, pp 898–902 | Cite as

Hamilton operators and homothetic motions inR 3

  • Yusuf Yayli
  • Nergiz Yaz
  • Murat Kemal Karacan
Article

Abstract

Quaternion is a division ring. It is shown that planes passing through the origin can be made a field with the quaternion product in R3. The Hamiltonian operators help us define the homothetic motions on these planes. New characterizations for these motions are investigated.

Key words

Hamilton operator homothetic motion quaternion 

Chinese Library Classification

O151.23 O316 O311 

2000 Mathematics Subject Classification

11R52 70B05 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [1]
    Pfaff Frank R. A commutative multiplication of number triplets[J].Amer Math Monthly, 2000,107:156–162.MathSciNetCrossRefGoogle Scholar
  2. [2]
    Agrawall O P. Hamilton operators and dual-number quaternions in spatial kinematic[J].Mech Mach Theory, 1987,22(6):569–575.CrossRefGoogle Scholar
  3. [3]
    Yayli Y. Homothetic motions atE 4[J].Mech Mach Theory, 1992,27(3):303–305.CrossRefGoogle Scholar
  4. [4]
    Hacisalihoglu H H. On the rolling of one curve or surface upon another[J].Proc Roy Irish Acad Sect A, 1971,71(2):13–16.MATHMathSciNetGoogle Scholar
  5. [5]
    Yayli Y, Hacisalihoglu H H, Ergin A A. On the division algebras inR 3[J].Algebras, Groups and Geometries, 2001,18:341–348.MathSciNetGoogle Scholar

Copyright information

© Editorial Committee of Applied Mathematics and Mechanics 2004

Authors and Affiliations

  • Yusuf Yayli
    • 1
  • Nergiz Yaz
    • 1
  • Murat Kemal Karacan
    • 1
  1. 1.Department of Mathematics, Faculty of SciencesAnkara UniversityTandoĝan, AnkaraTurkey

Personalised recommendations