Year 2016, Volume 4, Issue 1, Pages 43 - 51 2016-03-12

HOMOTHETIC MOTIONS IN THE GENERALIZED 3-SPACE
HOMOTHETIC MOTIONS IN THE GENERALIZED 3-SPACE

Mehdi Jafari [1]

1097 651

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.  

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
Darboux vektör, Genelleştirilmiş Hamilton operatör, Genelleştirilmiş kuaterniyon, homotetik hareket, Pol noktası
  • 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 ETWMS 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,
Journal Section Articles
Authors

Author: Mehdi Jafari

Bibtex @ { aubtdb262704, journal = {ANADOLU UNIVERSITY JOURNAL OF SCIENCE AND TECHNOLOGY –B Theoretical Sciences}, issn = {2146-0272}, eissn = {2146-0191}, address = {Eskişehir Teknik Üniversitesi}, year = {2016}, volume = {4}, pages = {43 - 51}, doi = {10.20290/btdb.15221}, title = {HOMOTHETIC MOTIONS IN THE GENERALIZED 3-SPACE}, key = {cite}, author = {Jafari, Mehdi} }
APA Jafari, M . (2016). HOMOTHETIC MOTIONS IN THE GENERALIZED 3-SPACE. ANADOLU UNIVERSITY JOURNAL OF SCIENCE AND TECHNOLOGY –B Theoretical Sciences, 4 (1), 43-51. DOI: 10.20290/btdb.15221
MLA Jafari, M . "HOMOTHETIC MOTIONS IN THE GENERALIZED 3-SPACE". ANADOLU UNIVERSITY JOURNAL OF SCIENCE AND TECHNOLOGY –B Theoretical Sciences 4 (2016): 43-51 <http://dergipark.org.tr/aubtdb/issue/24861/262704>
Chicago Jafari, M . "HOMOTHETIC MOTIONS IN THE GENERALIZED 3-SPACE". ANADOLU UNIVERSITY JOURNAL OF SCIENCE AND TECHNOLOGY –B Theoretical Sciences 4 (2016): 43-51
RIS TY - JOUR T1 - HOMOTHETIC MOTIONS IN THE GENERALIZED 3-SPACE AU - Mehdi Jafari Y1 - 2016 PY - 2016 N1 - doi: 10.20290/btdb.15221 DO - 10.20290/btdb.15221 T2 - ANADOLU UNIVERSITY JOURNAL OF SCIENCE AND TECHNOLOGY –B Theoretical Sciences JF - Journal JO - JOR SP - 43 EP - 51 VL - 4 IS - 1 SN - 2146-0272-2146-0191 M3 - doi: 10.20290/btdb.15221 UR - https://doi.org/10.20290/btdb.15221 Y2 - 2019 ER -
EndNote %0 ANADOLU UNIVERSITY JOURNAL OF SCIENCE AND TECHNOLOGY –B Theoretical Sciences HOMOTHETIC MOTIONS IN THE GENERALIZED 3-SPACE %A Mehdi Jafari %T HOMOTHETIC MOTIONS IN THE GENERALIZED 3-SPACE %D 2016 %J ANADOLU UNIVERSITY JOURNAL OF SCIENCE AND TECHNOLOGY –B Theoretical Sciences %P 2146-0272-2146-0191 %V 4 %N 1 %R doi: 10.20290/btdb.15221 %U 10.20290/btdb.15221
ISNAD Jafari, Mehdi . "HOMOTHETIC MOTIONS IN THE GENERALIZED 3-SPACE". ANADOLU UNIVERSITY JOURNAL OF SCIENCE AND TECHNOLOGY –B Theoretical Sciences 4 / 1 (March 2016): 43-51. https://doi.org/10.20290/btdb.15221