Open AccessThe critical points of the elastic energy among curves pinned at endpoints
Author(s) -
Kensuke Yoshizawa
Publication year - 2022
Publication title -
discrete and continuous dynamical systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.289
H-Index - 70
eISSN - 1553-5231
pISSN - 1078-0947
DOI - 10.3934/dcds.2021122
Subject(s) - inflection point , critical point (mathematics) , mathematics , elastic energy , energy (signal processing) , mathematical analysis , point (geometry) , geometry , physics , statistics , thermodynamics
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.