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Yıl 2020, Cilt: 8 Sayı: 2, 419 - 422, 27.10.2020

Gözde Özkan Tükel , Tunahan Turhan

Öz

Kaynakça

  • [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.
  • [2] D.A. Singer, Lectures on elastic curves and rods, In AIP Conference Proceedings Vol: 1002, No.1 (2008), 3-32.
  • [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.

Elastica in Galilean 3-Space

Yıl 2020, Cilt: 8 Sayı: 2, 419 - 422, 27.10.2020

Gözde Özkan Tükel , Tunahan Turhan

Öz

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 $G_{3}$.                                                    
                                    

Anahtar Kelimeler

Elastic curves Euler-Lagrange equations Galilean 3-space

Kaynakça

  • [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.
  • [2] D.A. Singer, Lectures on elastic curves and rods, In AIP Conference Proceedings Vol: 1002, No.1 (2008), 3-32.
  • [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.
Toplam 7 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Articles
Yazarlar

Gözde Özkan Tükel

Tunahan Turhan

Yayımlanma Tarihi 27 Ekim 2020
Gönderilme Tarihi 23 Şubat 2020
Kabul Tarihi 21 Ekim 2020
Yayımlandığı Sayı Yıl 2020 Cilt: 8 Sayı: 2

Kaynak Göster

APA Özkan Tükel, G., & Turhan, T. (2020). Elastica in Galilean 3-Space. Konuralp Journal of Mathematics, 8(2), 419-422.
AMA Özkan Tükel G, Turhan T. Elastica in Galilean 3-Space. Konuralp J. Math. Ekim 2020;8(2):419-422.
Chicago Özkan Tükel, Gözde, ve Tunahan Turhan. “Elastica in Galilean 3-Space”. Konuralp Journal of Mathematics 8, sy. 2 (Ekim 2020): 419-22.
EndNote Özkan Tükel G, Turhan T (01 Ekim 2020) Elastica in Galilean 3-Space. Konuralp Journal of Mathematics 8 2 419–422.
IEEE G. Özkan Tükel ve T. Turhan, “Elastica in Galilean 3-Space”, Konuralp J. Math., c. 8, sy. 2, ss. 419–422, 2020.
ISNAD Özkan Tükel, Gözde - Turhan, Tunahan. “Elastica in Galilean 3-Space”. Konuralp Journal of Mathematics 8/2 (Ekim 2020), 419-422.
JAMA Özkan Tükel G, Turhan T. Elastica in Galilean 3-Space. Konuralp J. Math. 2020;8:419–422.
MLA Özkan Tükel, Gözde ve Tunahan Turhan. “Elastica in Galilean 3-Space”. Konuralp Journal of Mathematics, c. 8, sy. 2, 2020, ss. 419-22.
Vancouver Özkan Tükel G, Turhan T. Elastica in Galilean 3-Space. Konuralp J. Math. 2020;8(2):419-22.
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