Variational analysis of inextensible elastic curves

TL;DR

This paper develops a variational framework for analyzing inextensible elastic curves by minimizing combined curvature and torsion energies, exploring critical points, and providing numerical examples relevant to applications.

Contribution

It introduces a variational approach to elastic curves with curvature and torsion penalties, including critical point analysis and numerical experiments.

Findings

Identification of critical points for elastic energy functionals

Numerical demonstrations of elastic curve configurations

Application-oriented examples illustrating theoretical results

Abstract

We minimize elastic energies on framed curves which penalize both curvature and torsion. We also discuss critical points using the infinite dimensional version of the Lagrange multipliers' method. Finally, some examples arising from the applications are discussed and also numerical experiments are presented.