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Dergiler / Konuralp Journal of Mathematics / 2020 / Cilt: 8 - Sayı: 2

Elastica in Galilean 3-Space

Gözde ÖZKAN TÜKEL
Tunahan TURHAN
Sayfa
419–422
Yayın Tarihi
2020-10-27
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Finally, we give an example for elastic curves in Galilean $3-$space $G_{3}$.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In this work, we aim to develop classical Euler-Bernoulli elastic curves in a non-Euclidean space.
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Temel Bulgular & Veri:So, we study the curvature energy action under some boundary conditions in the Galilean $3-$ space $G_{3}$.
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Sonuç & Katkı:Finally, we give an example for elastic curves in Galilean $3-$space $G_{3}$.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Elastic curves · Euler-Lagrange equations · Galilean 3-space

Abstract

In this work, we aim to develop classical Euler-Bernoulli elastic curves in a non-Euclidean space. So, we study the curvature energy action under some boundary conditions in the Galilean $3-$ space $G_{3}$. Then, we derive the Euler-Lagrange equation for bending energy functional acting on suitable curves in $G_{3}$. We solve this differential equation by using some solving methods in applied mathematics. Finally, we give an example for elastic curves in Galilean $3-$space $G_{3}$.

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Bu Makaleye Atıf Yap

TÜKEL, G. Ö., TURHAN, T. (2020). Elastica in Galilean 3-Space. Konuralp Journal of Mathematics, Cilt: 8 - Sayı: 2, 419–422. https://ajindex.com/articles/786446

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Kaynakça (7)

  1. T. Şahin, 2013. Intrinsic equations for a generalized relaxed elastic line on an oriented surface in the Galilean space, Acta Mathematica Scientia, Vol: 33, No.3 (2013), 701-711
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  3. I.M. Yaglom, A Simple Non-Euclidean Geometry and Physical Basis, (1979), Springer-Verlag, New York, 307p
  4. Y. Keleş, Galilean and Pseudo-Galilean Space Curves, Master Thesis, Karadeniz Technical University The Graduate School of Natural and Applied Sciences, (2004), Trabzon, TURKEY
  5. B.J. Pavkovic and I. Kamenarovic, The equiform differential geometry of curves in the Galilean space. Glasnik Matematicki Vol:22, No.2 (1987), 449-457
  6. P. A. Griffiths, P. A., Exterior differential systems and the calculus of variations, Vol: 25, (2013), Springer Science \& Business Media
  7. T. Şahin, and B. C. Dirisen, Position vectors of curves with recpect to Darboux frame in the Galilean space $G_{3}$, Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, Vol: 68, No. 2 (2019), 2079-2093.