Variational analysis of inextensible elastic curves

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.

References in corpus (6)

• Hamiltonians for curves
• Translation of Michael Sadowsky's paper "An elementary proof for the existence of a developable Möbius band and the attribution of the geometric problem to a variational problem"
• Functionals linear in curvature and statistics of helical proteins
• Force and moment balance equations for geometric variational problems on curves
• Solution of the Kirchhoff-Plateau problem
• Translation and interpretation of Michael Sadowsky's paper "Theory of elastically bendable inextensible bands with applications to the Möbius band"

Cited by in corpus (3)

• Elastic membranes spanning deformable boundaries
• Effects of surface tension and elasticity on critical points of the Kirchhoff-Plateau problem
• Existence of optimal flat ribbons