Lastly, we give explicitly the hyperelastic curves by integral according to the selected cylindrical coordinate systems in 3−dimensional lightlike cone using these Killing vector fields.
📌 3 Key Takeaways
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Objective & Hypothesis:We study hyperelastic curves known as a generalization of elastic curves in 3−dimensional lightlike cone which is a degenerate hypersurface in Minkowski 4−space as critical points of the cone curvature energy functional constructed with the r−th power of the cone curvature depending on the given boundary conditions for the natural number r ≥ 2.
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Key Findings & Data:We derive the Euler-Lagrange equations for the critical points of this functional that is namely the hyperelastic curves and solve completely the Euler-Lagrange equations by quadratures.
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Conclusion & Impact:Lastly, we give explicitly the hyperelastic curves by integral according to the selected cylindrical coordinate systems in 3−dimensional lightlike cone using these Killing vector fields.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables:Domain Parameters
Abstract
We study hyperelastic curves known as a generalization of elastic curves in 3−dimensional lightlike cone which is a degenerate hypersurface in Minkowski 4−space as critical points of the cone curvature energy functional constructed with the r−th power of the cone curvature depending on the given boundary conditions for the natural number r ≥ 2. We derive the Euler-Lagrange equations for the critical points of this functional that is namely the hyperelastic curves and solve completely the Euler-Lagrange equations by quadratures. Then, we construct Killing vector fields along the hyperelastic curves. Lastly, we give explicitly the hyperelastic curves by integral according to the selected cylindrical coordinate systems in 3−dimensional lightlike cone using these Killing vector fields.
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Cite This Article
YÜCESAN, A., KAĞIZMAN, S. T. (2022). Hyperelastic curves in 3−dimensional lightlike cone. Turkish Journal of Mathematics, Cilt: 46 - Sayı: 1, 47–58. https://ajindex.com/articles/607250
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