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Year 2016, Volume: 4 Issue: 1, 136 - 143, 15.04.2016
https://doi.org/10.36753/mathenot.421422

Abstract

References

  • [1] WARD, J. P., Quaternions and Cayley Algebrs and Applications, Kluwer Academic Publishers, Dordrecht, 1996.
  • [2] Bekar, M. and Yayli, Y., Involutions of Complexified Quaternions and Split Quaternions, Advances in Applied Clifford Algebras (2013), 23, 283–299.
  • [3] Bekar, M. and Yayli, Y., Dual-quaternion Involutions and Anti-Involutions, Advances in Applied Clifford Algebras (2013), 23, 577–592.
  • [4] Ell, T. A. and Sangwine, S. J., Quaternion Involutions and Anti-involutions, Computers and Mathematics with Applications (2007), 53, 137–143.
  • [5] Blaschke, W., Euclidian kinematics and non-Euclidian geometry I, II, Zeitschrift für Mathematik und Physik (1911), 60, 61–92.
  • [6] Pottman, H., and Wallner, J., Computational Line Geometry, Springer-Verlag, Heidelberg, 2001.
  • [7] Blaschke, W., Differential Geometrie and Geometrischke Grundlagen ven Einsteins Relativitasttheorie, Dover, New York, 1945.
  • [8] Fischer, I. S., Dual-Number Methods in Kinematics, Statics and Dynamics. Boca Raton London New York Washington D.C.: CRC Press, 1999.
  • [9] Hacisalihoglu, H.H., Hareket Geometrisi ve Kuaterniyonlar Teorisi, Gazi Universitesi Fen-Edb. Fakultesi, 1983.
  • [10] Veldkamp, G.R., On the use of dual numbers, vectors and matrices in instantaneous spatial kinematics, Mech. Mach. Theory (1976), 11(2), 141–156.

Dual-Quasi Elliptic Planar Motion

Year 2016, Volume: 4 Issue: 1, 136 - 143, 15.04.2016
https://doi.org/10.36753/mathenot.421422

Abstract

Dual-quaternions are an elegant and useful mathematical tools for representing rigid-body (screw)
motions in three-dimensional Euclidean space R
3
. The aim of this paper is to consider the algebra of dual
semi-quaternions with their basic properties and generalize the results of the Euclidean-planar motion
given by Blaschke and Grünwald to dual planar motion. 

References

  • [1] WARD, J. P., Quaternions and Cayley Algebrs and Applications, Kluwer Academic Publishers, Dordrecht, 1996.
  • [2] Bekar, M. and Yayli, Y., Involutions of Complexified Quaternions and Split Quaternions, Advances in Applied Clifford Algebras (2013), 23, 283–299.
  • [3] Bekar, M. and Yayli, Y., Dual-quaternion Involutions and Anti-Involutions, Advances in Applied Clifford Algebras (2013), 23, 577–592.
  • [4] Ell, T. A. and Sangwine, S. J., Quaternion Involutions and Anti-involutions, Computers and Mathematics with Applications (2007), 53, 137–143.
  • [5] Blaschke, W., Euclidian kinematics and non-Euclidian geometry I, II, Zeitschrift für Mathematik und Physik (1911), 60, 61–92.
  • [6] Pottman, H., and Wallner, J., Computational Line Geometry, Springer-Verlag, Heidelberg, 2001.
  • [7] Blaschke, W., Differential Geometrie and Geometrischke Grundlagen ven Einsteins Relativitasttheorie, Dover, New York, 1945.
  • [8] Fischer, I. S., Dual-Number Methods in Kinematics, Statics and Dynamics. Boca Raton London New York Washington D.C.: CRC Press, 1999.
  • [9] Hacisalihoglu, H.H., Hareket Geometrisi ve Kuaterniyonlar Teorisi, Gazi Universitesi Fen-Edb. Fakultesi, 1983.
  • [10] Veldkamp, G.R., On the use of dual numbers, vectors and matrices in instantaneous spatial kinematics, Mech. Mach. Theory (1976), 11(2), 141–156.
There are 10 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

Murat Bekar This is me

Publication Date April 15, 2016
Submission Date January 28, 2016
Published in Issue Year 2016 Volume: 4 Issue: 1

Cite

APA Bekar, M. (2016). Dual-Quasi Elliptic Planar Motion. Mathematical Sciences and Applications E-Notes, 4(1), 136-143. https://doi.org/10.36753/mathenot.421422
AMA Bekar M. Dual-Quasi Elliptic Planar Motion. Math. Sci. Appl. E-Notes. April 2016;4(1):136-143. doi:10.36753/mathenot.421422
Chicago Bekar, Murat. “Dual-Quasi Elliptic Planar Motion”. Mathematical Sciences and Applications E-Notes 4, no. 1 (April 2016): 136-43. https://doi.org/10.36753/mathenot.421422.
EndNote Bekar M (April 1, 2016) Dual-Quasi Elliptic Planar Motion. Mathematical Sciences and Applications E-Notes 4 1 136–143.
IEEE M. Bekar, “Dual-Quasi Elliptic Planar Motion”, Math. Sci. Appl. E-Notes, vol. 4, no. 1, pp. 136–143, 2016, doi: 10.36753/mathenot.421422.
ISNAD Bekar, Murat. “Dual-Quasi Elliptic Planar Motion”. Mathematical Sciences and Applications E-Notes 4/1 (April 2016), 136-143. https://doi.org/10.36753/mathenot.421422.
JAMA Bekar M. Dual-Quasi Elliptic Planar Motion. Math. Sci. Appl. E-Notes. 2016;4:136–143.
MLA Bekar, Murat. “Dual-Quasi Elliptic Planar Motion”. Mathematical Sciences and Applications E-Notes, vol. 4, no. 1, 2016, pp. 136-43, doi:10.36753/mathenot.421422.
Vancouver Bekar M. Dual-Quasi Elliptic Planar Motion. Math. Sci. Appl. E-Notes. 2016;4(1):136-43.

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