HOMOTHETIC MOTIONS IN THE GENERALIZED 3-SPACE
Üç ve dört boyutlu Öklid uzayinda, bir parametre homotetik hareketleri Yaylı’nın doktora tezin’de [15] tam olarak temın edilir. Burada biz bu fikri kulanarak, genelleştirilmiş 3-boyutlu uzayda bir parametre homotetik hareketi tanıtırdık. Genelleştirilmiş Hamilton operatörler ile, aynı zamanda Hamilton hareket tanımlar ve bu bir homototik hareket olduğunu göstermektedir.Bu hareketın bazı özelliklerini araştırdık ve gösterdik ki bu hareketin Darboux vektörü İki genelleştirilmiş kuaterniyonların çarpmasi yazilabilir
Anahtar Kelimeler:
Darboux vektör, Genelleştirilmiş Hamilton operatör, Genelleştirilmiş kuaterniyon, homotetik hareket, Pol noktası
HOMOTHETIC MOTIONS IN THE GENERALIZED 3-SPACE
A complete treatment of one parameter homothetic motions in three and four dimensional Euclidean spaces is provided in the Yayli's PhD thesis (Yaylı, 1988). Here we follow his idea to define one parameter homothetic motion in generalized 3-space By means of the generalized Hamilton operators, we also define a Hamilton motion and show that it is a homothetic motion. We investigate some properties of this motion and show that Darboux vector of the motion can be written as multiplication of two generalized quaternions.
___
- Bottema O, Roth B, Theorical kinematics, Oxford, New York; 1979.
- Hacisalihoglu H.H, On the rolling of one curve or surface upon another, Mathematical proceedings of the Royal Irish academy, 71A2; 13-17, 1971
- Jafari, M. On the properties of quasi-quaternion algebra, Communications faculty of science, university of Ankara, Series1, 63(1); 1-10, 2014.
- Jafari M, Yayli Y, Rotation in four dimensions via generalized Hamilton operators, Kuwait journal of science, 40(1); 67-79, 2013.
- Jafari M, Homothetic motions in Euclidean 3-space, Kuwait journal of science, 41(1); 65-73, Jafari M, Yayli Y, Homothetic Motions at E , International Journal contemporary of Mathematical Sciences, 5 (47); 2319-2326, 2010.
- Jafari M, Yayli Y, Generalized quaternions and rotation in 3-space ETWMS journal of pure ,TWMS journal of pure and applied mathematics, 6(2); 224-235, 2015.
- Jafari M, Split semi-quaternions algebra in semi-Euclidean 4-space, Cumhuriyet university faculty of science, 36 (1); 70-77, 2015.
- Jafari M, Yayli Y, One-parameter homothetic motions in the Minkowski 3-space, TWMS Journal of Applied and Engineering Mathematics, 6(1); 335-346, 2016.
- Kula L, Yayli Y, Split quaternions and rotations in semi-Euclidean spaceE, Journal of Korean , Journal of Korean , Journal of Korean mathematical society, 44(6); 1313-1327, 2007.
- Mortazaasl H, Jafari M, A study on semi-quaternions algebra in semi-Euclidean 4-space, mathematical science and application E-Notes, 1(2); 20-27, 2013.
- Müller H.R, Kinematik dersleri, Ankara üniversitesi fen fakultesi yaynları, Um. 96 (Mat No 2, Tosun M, Kucuk A, Gungor M.A, The homothetic motions in the Lorentz 3-space, Acta mathematica science, 26B(4); 711-719. 2006
- Yaylı Y, Homothetic motions at E , Mechanism and machine theory, 27(3); 303-305, 1992.
- Yaylı Y,Hamilton operators and Lie groups, Ph.D. thesis, Gazi University, Ankara, Turkey,
- ISSN: 2667-419X
- Yayın Aralığı: Yılda 2 Sayı
- Başlangıç: 2010
- Yayıncı: Eskişehir Teknik Üniversitesi
Sayıdaki Diğer Makaleler
Halil BERBER, Nilüfer Aksu ATEŞ, Müjgan Yaman ÖZKÜTÜK
ÜÇGENİN GERGONNE NOKTASI YARDIMIYLA ÜÇGENSEL FUZZY SAYILARI SIRALAMA YÖNTEMİ
COMPARISON OF METHODS OF ESTIMATING VARIANCE COMPONENTS IN BALANCED TWO-WAY RANDOM NESTED DESIGNS
Ebru Kaya BAŞAR, Mehmet Ziya FIRAT
METRİK KATEGORİDE PROJEKTİF OBJELER