Existence of free nonclosed Euler–Bernoulli elastica

DOI10.1016/0362-546X(93)90002-AzbMath0809.53006OpenAlexW2072007000MaRDI QIDQ4291639

Anders Linnér

Publication date: 28 March 1995

Published in: Nonlinear Analysis: Theory, Methods & Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0362-546x(93)90002-a

zbMATH Keywords

Jacobi elliptic functionsEuler-Bernoulli elasticatotal squared curvatureEmdem-Fowler equation

Mathematics Subject Classification ID

Curves in Euclidean and related spaces (53A04) Variational problems in applications to the theory of geodesics (problems in one independent variable) (58E10)

Related Items (12)

Morse theory for elastica ⋮ Extendability of Kirchhoff elastic rods in complete Riemannian manifolds ⋮ Polar tangential angles and free elasticae ⋮ Existence of planar curves minimizing length and curvature ⋮ Closed free hyperelastic curves in the hyperbolic plane and Chen-Willmore rotational hyper\-surfaces ⋮ Boundary value problems for Euler-Bernoulli planar elastica. A solution construction procedure ⋮ Elastic splines III: existence of stable nonlinear splines ⋮ Elastic curves and phase transitions ⋮ Curve-straightening and the Palais-Smale condition ⋮ Hamilton equations for elasticae in the Euclidean 3-space ⋮ A unique graph of minimal elastic energy ⋮ On the Gamma-convergence of some polygonal curvature functionals

Cites Work

• The total squared curvature of closed curves
• Energy, fairness, and a counterexample
• Curve-straightening in Riemannian manifolds
• Choosing nodes in parametric curve interpolation
• Stable and unstable elastica equilibrium and the problem of minimum curvature
• Curve-straightening in closed Euclidean submanifolds
• Curve straightening and a minimax argument for closed elastic curves
• Minimal-energy splines: I. Plane curves with angle constraints
• Curves in the Hyperbolic Plane and mean Curvature of Tori in 3-Space
• The Curve of Least Energy
• Knotted Elastic Curves in R ³
• Some Properties of the Curve Straightening Flow in the Plane
• Equilibria of the Curvature Functional and Manifolds of Nonlinear Interpolating Spline Curves
• Smooth Interpolating Curves of Prescribed Length and Minimum Curvature
• On the Computation of Nonlinear Spline Functions
• Variational Study of Nonlinear Spline Curves
• Minimization Problems and Linear and Nonlinear Spline Functions. I: Existence
• Minimization Problems and Linear and Nonlinear Spline Functions. II. Convergence

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