The hanging chain problem with respect to a circle

2024/05/21 by Rafael López, López, Rafael
Engineering · #49J05 #49K05 #53A04 #Differential Geometry (math.DG) #Elasticity and Wave Propagation #FOS: Mathematics

paper · pdf · doi:10.48550/arxiv.2405.12947

openalex publication_date 2024/05/21 · openalex created_date 2024/05/23 · openalex updated_date 2026/07/28

Abstract

Let \s¹ be a circle in Euclidean plane. We consider the problem of finding the shape of a planar curve which is an extremal of the potential energy that measures the distance to \s¹. We describe the shape of these curves distinguishing if the curves lie in the inside or outside of \s¹. We extend the problem for energies that are powers to the distance to \s¹.

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