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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
Finally, we give an example for elastic curves in Galilean $3-$space $G_{3}$.
📌 3 Key Takeaways
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Objective & Hypothesis:In this work, we aim to develop classical Euler-Bernoulli elastic curves in a non-Euclidean space.
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Key Findings & Data:So, we study the curvature energy action under some boundary conditions in the Galilean $3-$ space $G_{3}$.
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Conclusion & Impact:Finally, we give an example for elastic curves in Galilean $3-$space $G_{3}$.
🔬Design:Research Article
📍Scope:Comprehensive Sample
⚙️Variables: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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Cite This Article
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