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Journals / TWMS (Turkic World Mathematical Society) Journal of Applied and Engineering Mathematics / 2016 / Cilt: 6 - Sayı: 1

ONE-PARAMETER HOMOTHETIC MOTION IN THE MINKOWSKI 3-SPACE

Mehdi JAFAR
Yusuf YAYLI
Pages
87–94
DOI
—
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⚡ TL;DR(Too Long; Didn't Read)

We also obtain the Darbouxvector of the homothetic motion in E1and show that it can be written as multiplicationof two split quaternions.

📌 3 Key Takeaways

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Objective & Hypothesis:A one-parameter homothetic motion in three-dimensional Minkowski spaceis defined by means of the Hamilton operators.
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Key Findings & Data:We study some properties of this motionand show that it has only one pole point at every instant t.
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Conclusion & Impact:We also obtain the Darbouxvector of the homothetic motion in E1and show that it can be written as multiplicationof two split quaternions.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters

Abstract

A one-parameter homothetic motion in three-dimensional Minkowski spaceis defined by means of the Hamilton operators. We study some properties of this motionand show that it has only one pole point at every instant t. We also obtain the Darbouxvector of the homothetic motion in E1and show that it can be written as multiplicationof two split quaternions.

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Cite This Article

JAFAR, M., YAYLI, Y. (2016). ONE-PARAMETER HOMOTHETIC MOTION IN THE MINKOWSKI 3-SPACE. TWMS (Turkic World Mathematical Society) Journal of Applied and Engineering Mathematics, Cilt: 6 - Sayı: 1, 87–94. https://ajindex.com/articles/327551

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References (2)

  1. Kula,L. and Yayli,Y., (2005), Homothetic motions in semi-Euclidean space E4, Mathematical Proceed- 2 ings of the Royal Irish Academy, 105 A1, pp. 9-15. Kula,L. and Yayli,Y., (2007), Split quaternions and rotations in semi-Euclidean space E2, Journal of the Korean Mathematical Society, 44(6), pp. 1313-1327. Jafari,M. and Yayli,Y., (2014), Matrix Theory over the Split Quaternions, International journal of geometry, 3(2). Jafari,M., (2014), Homothetic motions in Euclidean 3-space, Kuwait journal of science, Vol. 41(1), pp. 65-73. Ozdemir,M. and Ergin,A.A., (2006), Rotation with unit timelike quaternions in Minkowski 3-space, Journal of Geometry and Physics, 56, pp. 322-336. Tosun,M., Kucuk,A. and Gungor,M.A., (2006), The Homothetic Motions in the Lorentz 3-space, Acta Mathematica Scientia, 26B(4), pp. 711-719. Yayli,Y., (1988),
  2. Hamilton operators and Lie groups, Ph.D. thesis, Gazi University, Ankara, Turkey.