Rotation in four dimensions via generalized Hamilton operators

Authors

  • MEHDI JAFARI Department of Mathematics, Faculty of Science, Ankara University, 06100 Ankara, Turkey
  • YUSUF YAYLI Department of Mathematics, Faculty of Science, Ankara University, 06100 Ankara, Turkey

Keywords:

Generalized quaternion, Hamilton operator, rotation

Abstract

ABSTRACT

In this paper, after a brief review of some algebraic properties of generalized quaternions, we investigated the properties of generalized Hamilton operators and we considered how the generalized quaternions can be used to described the rotation in 4-dimensional space  .

 

References

REFERENCES

Adler, S. L. 1995. Quaternionic quantum mechanics and quantum fields. Oxford University Press Inc., New York. Pp. 65.

Agrawal, O. P. 1987. Hamilton operators and dual-number-quaternions in spatial kinematics. Mechanism and Machine Theory 22 (6): 569-575.

Farebrother, R. W., GroB, J. & Troschke, S. 2003. Matrix representation of quaternions. Linear Algebra and its Applications 362: 251-255.

Girard, P. R. 2007. Quaternions, Clifford algebras relativistic physics. Birkhäuser verlag AG, Switzerland Part of Springer Science+Business Media. Pp. 18.

Groβ, J., Trenkler, G. & Troschke, S. 2001. Quaternions: futher contributions to a matrix oriented approach, Linear Algebra and its Applications 326: 205-213.

Jafari, M. & Yayli, Y. 2010a. Hamilton operators and generalized quaternions, 8th Geometry Conference, Antalya, Turkey. Pp. 103.

Jafari, M. & Yayli, Y. 2010b. Homothetic motions at International Journal Contemporary of Mathematics Sciences. 5(47): 2319-2326.

Jafari, M., Mortazaasl, H. & Yayli, Y. 2011. De-Moivre’s formula for matrices of quaternions. JP Journal of Algebra, Number Theory and Applications 21(1): 57-67.

Kula, L. & Yayli, Y. 2007. Split quaternions and rotations in semi-Euclidean space , Journal of Korean Mathematical Society 44(6): 1313-1327.

Pottman, H. & Wallner, J. 2000. Computational line geometry. Springer-Verlag, New York. Pp. 535.

Rosenfeld, B. A. 1997. Geometry of Lie groups. Kluwer Academic Publishers, Dordrecht. Pp. 46.

Savin, D., Flaut, C. & Ciobanu, C. 2009. Some properties of the symbol algebras, Carpathian Journal Mathematics 25(2): 239-245.

Unger, T. & Markin, N. 2008. Quadratic forms and space-time block codes from generalized quaternion and biquaternion algebras. IEEE Transactions on Information Theory, 57 (9): 6148-6156.

Ward, J. P. 1997. Quaternions and Cayley numbers algebra and applications, Kluwer Academic Publishers, London. Pp.78.

Weiner, J. L. & Wilkens, G. R. 2005. Quaternions and rotations in . Mathematical Association of America 12: 69-76.

Yayli, Y. 1992. Homothetic motions at Mechanism and Machine Theory 27(3): 303-305.

Zhang, F. 1997. Quaternions and matrices of quaternions. Linear Algebra and its Applications 251: 21-57.

Downloads

Published

03-09-2013