Kirchhoff elastic rods in a Riemannian manifold

DOI10.2748/TMJ/1113247562zbMath1011.58008OpenAlexW1980877775WikidataQ115227300 ScholiaQ115227300MaRDI QIDQ1848685

Satoshi Kawakubo

Publication date: 13 November 2002

Published in: Tôhoku Mathematical Journal. Second Series (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.2748/tmj/1113247562

zbMATH Keywords

variational problemRiemannian manifoldthree-dimensional Euclidean spaceenergy of uniform symmetric Kirchhoff elastic rodsexistence and regularity of minimizers

Mathematics Subject Classification ID

Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Global Riemannian geometry, including pinching (53C20) Variational problems in applications to the theory of geodesics (problems in one independent variable) (58E10)

Related Items (5)

Kirchhoff elastic rods in the three-sphere ⋮ Extendability of Kirchhoff elastic rods in complete Riemannian manifolds ⋮ Kirchhoff elastic rods in five-dimensional space forms whose centerlines are not helices ⋮ Kirchhoff elastic rods in higher-dimensional space forms ⋮ GLOBAL SOLUTIONS OF THE EQUATION OF THE KIRCHHOFF ELASTIC ROD IN SPACE FORMS

Cites Work

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• The total squared curvature of closed curves
• Curve-straightening in Riemannian manifolds
• Ordinary differential equations of non-linear elasticity. II: Existence and regularity theory for conservative boundary value problems
• Stability and bifurcation of circular Kirchhoff elastic rods
• Elasticae in a Riemannian submanifold
• Knot Types, Homotopies and Stability of Closed Elastic Rods
• Lagrangian Aspects of the Kirchhoff Elastic Rod

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