Elastica in Galilean 3-Space

Year 2020, Volume: 8 Issue: 2, 419 - 422, 27.10.2020

Gözde Özkan Tükel Tunahan Turhan

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

References

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