Tessarines and Homothetic Exponential Motions In 4-Dimensioal Euclidean space

Faik Babadağ

Tessarines and Homothetic Exponential Motions In 4-Dimensioal Euclidean space

Yıl 2017, Cilt: 10 Sayı: 1, 0 - 0, 30.06.2017

Öz

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.

Anahtar Kelimeler

Tessarines, Homothetic exponential motion, Hyper surface, Regular curve.

Kaynakça

: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).

Yıl 2017, Cilt: 10 Sayı: 1, 0 - 0, 30.06.2017

Faik Babadağ

Öz

Anahtar Kelimeler

Geometri

Kaynakça

: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).

Toplam 15 adet kaynakça vardır.

Ayrıntılar

Bölüm	Makaleler
Yazarlar	Faik Babadağ
Yayımlanma Tarihi	30 Haziran 2017
Yayımlandığı Sayı	Yıl 2017 Cilt: 10 Sayı: 1

Kaynak Göster

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. Haziran 2017;10(1).
Chicago	Babadağ, Faik. “Tessarines and Homothetic Exponential Motions In 4-Dimensioal Euclidean Space”. Beykent Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 10, sy. 1 (Haziran 2017).
EndNote	Babadağ F (01 Haziran 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, c. 10, sy. 1, 2017.
ISNAD	Babadağ, Faik. “Tessarines and Homothetic Exponential Motions In 4-Dimensioal Euclidean Space”. Beykent Üniversitesi Fen ve Mühendislik Bilimleri Dergisi 10/1 (Haziran 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, c. 10, sy. 1, 2017.
Vancouver	Babadağ F. Tessarines and Homothetic Exponential Motions In 4-Dimensioal Euclidean space. BUJSE. 2017;10(1).