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MATRICES OF GENERALIZED DUAL QUATERNIONS

Year 2015, Volume: 3 Issue: 2, 110 - 121, 01.10.2015

Abstract

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.

References

  • [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.
Year 2015, Volume: 3 Issue: 2, 110 - 121, 01.10.2015

Abstract

References

  • [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.
There are 20 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Mehdi Jafarı This is me

Publication Date October 1, 2015
Submission Date July 10, 2014
Published in Issue Year 2015 Volume: 3 Issue: 2

Cite

APA Jafarı, M. (2015). MATRICES OF GENERALIZED DUAL QUATERNIONS. Konuralp Journal of Mathematics, 3(2), 110-121.
AMA Jafarı M. MATRICES OF GENERALIZED DUAL QUATERNIONS. Konuralp J. Math. October 2015;3(2):110-121.
Chicago Jafarı, Mehdi. “MATRICES OF GENERALIZED DUAL QUATERNIONS”. Konuralp Journal of Mathematics 3, no. 2 (October 2015): 110-21.
EndNote Jafarı M (October 1, 2015) MATRICES OF GENERALIZED DUAL QUATERNIONS. Konuralp Journal of Mathematics 3 2 110–121.
IEEE M. Jafarı, “MATRICES OF GENERALIZED DUAL QUATERNIONS”, Konuralp J. Math., vol. 3, no. 2, pp. 110–121, 2015.
ISNAD Jafarı, Mehdi. “MATRICES OF GENERALIZED DUAL QUATERNIONS”. Konuralp Journal of Mathematics 3/2 (October 2015), 110-121.
JAMA Jafarı M. MATRICES OF GENERALIZED DUAL QUATERNIONS. Konuralp J. Math. 2015;3:110–121.
MLA Jafarı, Mehdi. “MATRICES OF GENERALIZED DUAL QUATERNIONS”. Konuralp Journal of Mathematics, vol. 3, no. 2, 2015, pp. 110-21.
Vancouver Jafarı M. MATRICES OF GENERALIZED DUAL QUATERNIONS. Konuralp J. Math. 2015;3(2):110-21.
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