Elastica in Galilean 3-Space

Authors : Gözde ÖZKAN TÜKEL, Tunahan TURHAN

Pages : 419-422

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Publication Date : 2020-10-27

Article Type : Research Paper

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 $G_{3}$.                                                                                         
Keywords : Elastic curves, Euler Lagrange equations, Galilean 3 space