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Tessarines and Homothetic Exponential Motions In 4-Dimensioal Euclidean space

Year 2017, Volume: 10 Issue: 1, 0 - 0, 30.06.2017

Abstract

In this study, for tessarines in 4-dimension Euclidean space, we describe a variety of algebraic properties and give a matrix that is similar to Hamilton operators and a new exponential motion is defined by this matrix. Then, this exponential motion is proven to be homothetic exponential motion. For this one parameter homothetic exponential motion, we defined some theorems about velocities, pole points, and pole curves. Finally, It is found that this exponential defined by the regular curve of order n curve lying curves on the hypersurface M, at every t- instant, has only one acceleration centre of order (n-1).
Due to the way with tessarines in which the matter is given , the study gives some formulas facts about homothetic exponential motion and variety of algebraic propertieswhich are not generally known.

References

  • :James Cockle, On Certain Functions Resembling Quaternions and on a New Imaginary in Algebra, Philosophical magazine, series3,London-Dublin-Edinburgh , 1848.
  • : James Cockle, On a New Imaginary in Algebra 34:37--47, Philosophical magazine, series3,London-Dublin-Edinburgh , 1849.
  • : James Cockle, On the Symbols of Algebra and on the Theory of Tessarines 34:406--10, Philosophical magazine, series3,London-Dublin-Edinburgh , 1849.
  • : James Cockle, On Impossible Equations, on Impossible Quantities and on Tessarines 37:281--3, Philosophical magazine, series3,London-Dublin-Edinburgh , 1850.
  • : James Cockle, On the True Amplitude of a Tessarine 38:290--2, Philosophical magazine, series3,London-Dublin-Edinburgh , 1850.
  • : Clifford, W. and McMahon, J.J., The rolling of one curve or surface up on another. Am. Math. 68(23A2134), 338-341, 1961.
  • : Müller, H.R., Zur Bewenguns geometrie in Röümen Höhere dimensions. Mh. Math. 70 band, 1 helf, 47-57, 1966.
  • : Olcaylar, I., Homothetic motions in three dimensional space. Asc. Thesis. Faculty of Science, Ankara, Turkey, Middle East Technical Univ, 1967.
  • : Aydın, A.P., Homothetic exponential motions and their velocities. The Journal of Fırat University, 2(2), 33-39, 1987.
  • : Asil, V., Velocities of dual homothetic exponential motions in ID³ . Iranian Journal of Science & Technology, Transaction A, Vol. 31. No. A4, 2007.
  • : H.H.Hacısalihoglu, On The Rolling of one curve or surface upon another. Mathematical Proceeding of the R. Irish Acad, vol. 71(2),13-17.(1971).
  • : H.H.Hacısalihoglu, Motions and Quaternions theory. Gazi ¨University, Ankara.(1983).
  • : L. Kula, Y. Yayli, Homothetic Motions in semi - Euclidean spaces E₂⁴. Mathematical Proceeding of the R. Irish Academy, Vol. 105, section A, Num.1,9-15.(2005).
  • : O.P. Agrawal, Hamilton Operators and Dual Quaternions in Spatial Kinematics, Mech-Mach Theory (22), 569-575.(1987).
  • : D. Tascı,Lineer algebra,3.Academic Pres, Selcuk University,142-155,(2005).
Year 2017, Volume: 10 Issue: 1, 0 - 0, 30.06.2017

Abstract

References

  • :James Cockle, On Certain Functions Resembling Quaternions and on a New Imaginary in Algebra, Philosophical magazine, series3,London-Dublin-Edinburgh , 1848.
  • : James Cockle, On a New Imaginary in Algebra 34:37--47, Philosophical magazine, series3,London-Dublin-Edinburgh , 1849.
  • : James Cockle, On the Symbols of Algebra and on the Theory of Tessarines 34:406--10, Philosophical magazine, series3,London-Dublin-Edinburgh , 1849.
  • : James Cockle, On Impossible Equations, on Impossible Quantities and on Tessarines 37:281--3, Philosophical magazine, series3,London-Dublin-Edinburgh , 1850.
  • : James Cockle, On the True Amplitude of a Tessarine 38:290--2, Philosophical magazine, series3,London-Dublin-Edinburgh , 1850.
  • : Clifford, W. and McMahon, J.J., The rolling of one curve or surface up on another. Am. Math. 68(23A2134), 338-341, 1961.
  • : Müller, H.R., Zur Bewenguns geometrie in Röümen Höhere dimensions. Mh. Math. 70 band, 1 helf, 47-57, 1966.
  • : Olcaylar, I., Homothetic motions in three dimensional space. Asc. Thesis. Faculty of Science, Ankara, Turkey, Middle East Technical Univ, 1967.
  • : Aydın, A.P., Homothetic exponential motions and their velocities. The Journal of Fırat University, 2(2), 33-39, 1987.
  • : Asil, V., Velocities of dual homothetic exponential motions in ID³ . Iranian Journal of Science & Technology, Transaction A, Vol. 31. No. A4, 2007.
  • : H.H.Hacısalihoglu, On The Rolling of one curve or surface upon another. Mathematical Proceeding of the R. Irish Acad, vol. 71(2),13-17.(1971).
  • : H.H.Hacısalihoglu, Motions and Quaternions theory. Gazi ¨University, Ankara.(1983).
  • : L. Kula, Y. Yayli, Homothetic Motions in semi - Euclidean spaces E₂⁴. Mathematical Proceeding of the R. Irish Academy, Vol. 105, section A, Num.1,9-15.(2005).
  • : O.P. Agrawal, Hamilton Operators and Dual Quaternions in Spatial Kinematics, Mech-Mach Theory (22), 569-575.(1987).
  • : D. Tascı,Lineer algebra,3.Academic Pres, Selcuk University,142-155,(2005).
There are 15 citations in total.

Details

Journal Section Articles
Authors

Faik Babadağ

Publication Date June 30, 2017
Published in Issue Year 2017 Volume: 10 Issue: 1

Cite

APA Babadağ, F. (2017). Tessarines and Homothetic Exponential Motions In 4-Dimensioal Euclidean space. Beykent Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, 10(1).
AMA Babadağ F. Tessarines and Homothetic Exponential Motions In 4-Dimensioal Euclidean space. BUJSE. June 2017;10(1).
Chicago Babadağ, Faik. “Tessarines and Homothetic Exponential Motions In 4-Dimensioal Euclidean Space”. Beykent Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 10, no. 1 (June 2017).
EndNote Babadağ F (June 1, 2017) Tessarines and Homothetic Exponential Motions In 4-Dimensioal Euclidean space. Beykent Üniversitesi Fen ve Mühendislik Bilimleri Dergisi 10 1
IEEE F. Babadağ, “Tessarines and Homothetic Exponential Motions In 4-Dimensioal Euclidean space”, BUJSE, vol. 10, no. 1, 2017.
ISNAD Babadağ, Faik. “Tessarines and Homothetic Exponential Motions In 4-Dimensioal Euclidean Space”. Beykent Üniversitesi Fen ve Mühendislik Bilimleri Dergisi 10/1 (June 2017).
JAMA Babadağ F. Tessarines and Homothetic Exponential Motions In 4-Dimensioal Euclidean space. BUJSE. 2017;10.
MLA Babadağ, Faik. “Tessarines and Homothetic Exponential Motions In 4-Dimensioal Euclidean Space”. Beykent Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, vol. 10, no. 1, 2017.
Vancouver Babadağ F. Tessarines and Homothetic Exponential Motions In 4-Dimensioal Euclidean space. BUJSE. 2017;10(1).