Stability results for constrained calculus of variations problems: an analysis of the twisted elastic loop

DOI10.1098/RSPA.2004.1435zbMath1145.74373OpenAlexW1981742772MaRDI QIDQ5422935

Kathleen A. Hoffman

Publication date: 30 October 2007

Published in: Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1098/rspa.2004.1435

zbMATH Keywords

stabilityconstrained variational principlesdistinguished diagramsElastic loop

Mathematics Subject Classification ID

Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Energy minimization in equilibrium problems in solid mechanics (74G65) Bifurcation and buckling (74G60) Existence theories for optimal control problems involving partial differential equations (49J20)

Related Items (4)

Instability paths in the Kirchhoff-Plateau problem ⋮ Fractional variational principle of Herglotz for a new class of problems with dependence on the boundaries and a real parameter ⋮ A non-standard class of variational problems of Herglotz type ⋮ Bifurcation Analysis of the Oblique Shock Wave in the Supersonic Flow Over a Wedge from a Calculus of Variation Approach

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Three-dimensional shapes of looped DNA
• Restricted quadratic forms, inertia theorems, and the Schur complement
• Instability and self-contact phenomena in the writhing of clamped rods.
• Stability of solutions of nonlinear equations
• Stability predictions through a succession of folds
• Stability of Two Planar Loop Elasticas
• Optimal Large-Angle Single-Axis Rotational Maneuvers of Flexible Spacecraft
• Path following near bifurcation
• Isoperimetric conjugate points with application to the stability of DNA minicircles
• Knot Types, Homotopies and Stability of Closed Elastic Rods
• Nonlinear problems of elasticity

This page was built for publication: Stability results for constrained calculus of variations problems: an analysis of the twisted elastic loop