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A Study on a Generalized Relaxed Curvature Energy Action

Year 2018, Volume: 22 Issue: Special, 541 - 546, 05.10.2018

Gözde Özkan Tükel , Ahmet Yücesan

https://izlik.org/JA76YU85UH

Abstract

We investigate the variational problem of the generalized relaxed elastic line defined as the problem of finding critical points of the functional obtained by adding the twisting energy to the bending energy functional, on a non-degenerate surface in Minkowski 3-space. There arise two different situations for the curve $\alpha $ given on any non-degenerate surface S in Minkowski 3-space according to the absolute value expression in the curvature and torsion formulas. We study the problem for both cases and as a result we characterize the generalized relaxed elastic line with an Euler-Lagrange equation and 3 boundary conditions in both cases. Finally, we search special solutions for the differential equation system obtained with regard to the geodesic curvature, geodesic torsion and normal curvature of the curve.

Keywords

Generalized relaxed elastic line Euler-Lagrange equations; Variational calculus

References

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  • [2] Nickerson, H.K., Manning G.S., 1988. Intrinsic Equations for a Relaxed Elastic Line on an Oriented Surface. Geom. Dedicata, 27(2) 127-136.
  • [3] Yücesan, A., Özkan, G., 2012. Generalized Relaxed Elastic Line on an Oriented Surface. Ukranian Mathematical Journal, 64(8) 1121-1131.
  • [4] Akutagawa, K., Nishikawa S., 1990. The Gauss map and spacelike surfaces with prescribed mean curvature in Minkowski 3-space. Tohoku Math. J., 42 67-82.
  • [5] Lopez, R., 2014. Differential Geometry of Curves and Surfaces in Lorentz-Minkowski Space. International Electronic Journal of Geometry, 7(1) 44-107.
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  • [8] Özkan, G., Yücesan A., 2014. Relaxed Hyperelastic Curves on a Non-degenerate Surface. Mediterr. J. Math., 11 1241-1250.
There are 8 citations in total.

Details

Authors

Gözde Özkan Tükel

Ahmet Yücesan

Publication Date October 5, 2018
IZ https://izlik.org/JA76YU85UH
Published in Issue Year 2018 Volume: 22 Issue: Special

Cite

APA Özkan Tükel, G., & Yücesan, A. (2018). A Study on a Generalized Relaxed Curvature Energy Action. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, 22, 541-546. https://izlik.org/JA76YU85UH
AMA 1.Özkan Tükel G, Yücesan A. A Study on a Generalized Relaxed Curvature Energy Action. J. Nat. Appl. Sci. 2018;22:541-546. https://izlik.org/JA76YU85UH
Chicago Özkan Tükel, Gözde, and Ahmet Yücesan. 2018. “A Study on a Generalized Relaxed Curvature Energy Action”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 22 (October): 541-46. https://izlik.org/JA76YU85UH.
EndNote Özkan Tükel G, Yücesan A (October 1, 2018) A Study on a Generalized Relaxed Curvature Energy Action. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 22 541–546.
IEEE [1]G. Özkan Tükel and A. Yücesan, “A Study on a Generalized Relaxed Curvature Energy Action”, J. Nat. Appl. Sci., vol. 22, pp. 541–546, Oct. 2018, [Online]. Available: https://izlik.org/JA76YU85UH
ISNAD Özkan Tükel, Gözde - Yücesan, Ahmet. “A Study on a Generalized Relaxed Curvature Energy Action”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi 22 (October 1, 2018): 541-546. https://izlik.org/JA76YU85UH.
JAMA 1.Özkan Tükel G, Yücesan A. A Study on a Generalized Relaxed Curvature Energy Action. J. Nat. Appl. Sci. 2018;22:541–546.
MLA Özkan Tükel, Gözde, and Ahmet Yücesan. “A Study on a Generalized Relaxed Curvature Energy Action”. Süleyman Demirel Üniversitesi Fen Bilimleri Enstitüsü Dergisi, vol. 22, Oct. 2018, pp. 541-6, https://izlik.org/JA76YU85UH.
Vancouver 1.Gözde Özkan Tükel, Ahmet Yücesan. A Study on a Generalized Relaxed Curvature Energy Action. J. Nat. Appl. Sci. [Internet]. 2018 Oct. 1;22:541-6. Available from: https://izlik.org/JA76YU85UH

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