MATRICES OF GENERALIZED DUAL QUATERNIONS

MATRICES OF GENERALIZED DUAL QUATERNIONS

After a brief review of some algebraic properties of a generalized dual quaternion, we investigate properties of matrix associated with a gener- alized dual quaternion and examine De Moivre's formula for this matrix, from which the n-th power of such a matrix can be determined. We give the relation between the powers of these matrices.

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  • [1] Agrawal O. P., Hamilton operators and dual-number-quaternions in spatial kinematics, Mech- anism and machine theory, 22, no.6 (1987) 569-575.
  • [2] Akyar B., Dual Quaternions in Spatial Kinematics in an Algebraic Sense, Turk jornal of mathemathics, 32 (2008) 373-391.
  • [3] Ata E., Yayli y., Dual unitary matrices and unit dual quaternions, Di erential geometry- dynamical system, 10 (2008) 1-12.
  • [4] Cho E., De-Moivre Formula for Quaternions, Applied mathematics letters, Vol. 11(6) (1998) 33-35.
  • [5] Cli ord W., Preliminary sketch of biquaternions. Proc. of london Math. Soc. No.10, (1873) 381-395.
  • [6] Jafari M., Yayli Y., Hamilton operators and generalized quaternions, 8. Geometri Sem- pozyumu, 29 Apr.-2 May 2010, Antaliya, Turkey.
  • [7] Jafari M., Yayli Y., Dual generalized quaternions in spatial kinematics. 41st Annual Iranian Math. Conference, 12-15 Sep. 2010, Urmia, Iran.
  • [8] Jafari M., Generalized Screw Transformation and Its Applications in Robotics, Journal of Advanced Technology Sciences, Vol. 4 (2) (2015) 34-46.
  • [9] Jafari M., Meral M., Yayli Y., Matrix reperesentaion of dual quaternions, Gazi university journal of science, 26(4):535-542 (2013).
  • [10] Jafari M., Mortazaasl H., Yayli Y., De Moivre's Formula for Matrices of Quaternions, JP journal of algebra, number theory and applications, Vol.21(1) (2011)57-67.
  • [11] Kabadayi H., Yayli y., De-Moivre's Formula for Dual Quaternions, Kuwait journal of science & technology, Vol. 38(1) 1(2011) 15-23.
  • [12] Kotel nikov A.P., Vintovoe Schislenie i Nikotoriya Prilozheniye evo k geometrie i mechaniki, Kazan, 1895.
  • [13] Mortazaasl H., Jafari M., Yayli Y., Some Algebraic properties of dual generalized quaternions algebra, Far east journal of Mathematical science, Vol. 69 (2), (2012) 307-318.
  • [14] Ozdemir M., The Roots of a Split Quaternion, Applied mathematics letters, 22(2009) 258-263.
  • [15] Pennestri E., Stefanelli R., Linear algebra and numerical algorithms using dual numbers, University of Roma, Italy.
  • [16] Rashidi M., Shahsavari M., Jafari M., The E. Study mapping for directed lines in 3-space, International Research journal of applied and basic sciences, Vol. 5(11) 1374-1379 (2013).
  • [17] Study e., Von Den bewegungen und umlegungen, Mathematische Annalen 39 (1891) 441-564.
  • [18] Veldkamp G.R., On the use of dual numbers, vectors and matrices in instantaneous spatial kinematics, Mechanism and machine theory, 11 (1976) 141-156.
  • [19] Ward J. P., Quaternions and Cayley numbers algebra and applications, Kluwer Academic Publishers, London, 1997.
  • [20] Yang A.T., Freudenstein F., Application of dual-number quaternion algebra to the analysis of spatial mechanisms. ASME Journal of applied Mechnics 86E (2)(1964) 300-308.