Öz
In this study, by using tessarines in 4-dimension semi-Euclidean space, we describe a variety of algebraic properties and give a matrix that is similar to Hamilton operators and we show that the hypersurfaces are obtained and a new motion is defined in
𝐸42. Then, this motion is proven to be homothetic motion. For this one parameter homothetic motion, we defined some theorems about velocities, pole points, and pole curves. Finally, It is found that this motion defined by the regular curve of order r on the hypersurface 𝑀𝑖3, at every 𝑡- instant, has only one acceleration centre of order (𝑟 −1). Due to the way in which the matter is given with tessarines, the study gives some formulas, facts and properties about homothetic motion and variety of algebraic properties which are not generally known.
Anahtar Kelimeler
Kaynakça
- [1] J. Cockle, On Certain Functions Resembling Quaternions and on a New Imaginary in Algebra, Philosophical magazine, LondonDublin-Edinburgh, 1848.
- [2] J. Cockle, On a New Imaginary in Algebra Philosophical magazine, series3, London-Dublin-Edinburgh, 34, pp. 37--47, 1849.
- [3] J. Cockle, On the Symbols of Algebra and on the Theory of Tessarines, 34, pp. 406-410, Philosophical magazine, series3, London-Dublin-Edinburgh, 1849.
- [4] J. Cockle, On Impossible Equations, on Impossible Quantities and on Tessarines, ,Philosophical magazine, London-DublinEdinburgh, 1850.
- [5] J. Cockle, On the True Amplitude of a Tessarine, Philosophical magazine, London-Dublin-Edinburgh, 1850.
- [6] Y. Yaylı , Homothetic Motions at E4. Mech. Mach. Theory., 27 (3), 303-305, 1992.
- [7] F. Babadağ, Homothetic Motions And Bicomplex Numbers, Algebras, Groups And Geometrıes, Vol. 26, Number 4,193-201, 2009.
- [8] F. Babadağ, Y. Yaylı and N. Ekmekci, Homothetic Motions at (E ⁸ ) with Bicomplex Numbers (C ₃ ), Int. J. Contemp. Math. Sciences, Vol. 4, no. 33, 1619 - 1626, 2009.
- [9] F. Babadağ, The Real Matrices forms of the Bicomplex Numbers and Homothetic Exponential motions, Journal of Advances in Mathematics, ISSN 2347-1921, Vol 8, No. 1, 1401 - 1406, 2014.
- [10] B. O'Neill, Semi-Riemannian geometry, Academic Press, New York, 1983.
Öz
Bu çalışmada, 4 boyutlu yarı Öklid uzayında tessarinesleri kullanarak, Hamilton operatörlerine benzer bir matris verdik ve çeşitli cebirsel özelliklerini tanımladık. Daha sonra bu hareketin homotetik hareket olabilmesi ispatlandı. Bir parametreli homotetik hareket için, pol noktaları , pol eğrileri ve hız merkezleri hakkında bazı teoremler tanımladık. Sonunda, her 𝑡 anında, bir 𝑀𝑖3 hiperyüzeyi üzerinde eğrilerin türevleri ve 𝑟’ inci dereceden regular eğriler tarafından tanımlanan hareketin sadece (𝑟 − 1)’ inci derecen bir hız merkezine sahip olduğu bulundu. Tessarinesler ile verilen konudaki yöntemden dolayı, çalışma homotetik hareket hakkında bilinmeyen cebirsel özellikleri ve bazı formulleri , gerçekleri ve özellikleri veriyor.
Anahtar Kelimeler
Kaynakça
- [1] J. Cockle, On Certain Functions Resembling Quaternions and on a New Imaginary in Algebra, Philosophical magazine, LondonDublin-Edinburgh, 1848.
- [2] J. Cockle, On a New Imaginary in Algebra Philosophical magazine, series3, London-Dublin-Edinburgh, 34, pp. 37--47, 1849.
- [3] J. Cockle, On the Symbols of Algebra and on the Theory of Tessarines, 34, pp. 406-410, Philosophical magazine, series3, London-Dublin-Edinburgh, 1849.
- [4] J. Cockle, On Impossible Equations, on Impossible Quantities and on Tessarines, ,Philosophical magazine, London-DublinEdinburgh, 1850.
- [5] J. Cockle, On the True Amplitude of a Tessarine, Philosophical magazine, London-Dublin-Edinburgh, 1850.
- [6] Y. Yaylı , Homothetic Motions at E4. Mech. Mach. Theory., 27 (3), 303-305, 1992.
- [7] F. Babadağ, Homothetic Motions And Bicomplex Numbers, Algebras, Groups And Geometrıes, Vol. 26, Number 4,193-201, 2009.
- [8] F. Babadağ, Y. Yaylı and N. Ekmekci, Homothetic Motions at (E ⁸ ) with Bicomplex Numbers (C ₃ ), Int. J. Contemp. Math. Sciences, Vol. 4, no. 33, 1619 - 1626, 2009.
- [9] F. Babadağ, The Real Matrices forms of the Bicomplex Numbers and Homothetic Exponential motions, Journal of Advances in Mathematics, ISSN 2347-1921, Vol 8, No. 1, 1401 - 1406, 2014.
- [10] B. O'Neill, Semi-Riemannian geometry, Academic Press, New York, 1983.
Ayrıntılar
| Konular | Mühendislik |
|---|---|
| Bölüm | Makaleler |
| Yazarlar | |
| Yayımlanma Tarihi | 28 Aralık 2017 |
| Yayımlandığı Sayı | Yıl 2017 Cilt: 10 Sayı: 2 |
Kaynak Göster
Bu eser Creative Commons Atıf 4.0 Uluslararası Lisansı ile lisanslanmıştır.