The critical points of the elastic energy among curves pinned at endpoints
Differential Geometry
2021-06-25 v3 Analysis of PDEs
Classical Analysis and ODEs
Abstract
In this paper we find curves minimizing the elastic energy among curves whose length is fixed and whose ends are pinned. Applying the shooting method, we can identify all critical points explicitly and determine which curve is the global minimizer. As a result we show that the critical points consist of wavelike elasticae and the minimizers do not have any loops or interior inflection points.
Cite
@article{arxiv.2103.11607,
title = {The critical points of the elastic energy among curves pinned at endpoints},
author = {Kensuke Yoshizawa},
journal= {arXiv preprint arXiv:2103.11607},
year = {2021}
}
Comments
22 pages, 4 figures