Motion of elastic wire with thickness

zbMath1214.35069MaRDI QIDQ601289

Mitsuru Sugimoto, Norihito Koiso

Publication date: 4 November 2010

Published in: Osaka Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.ojm/1285334475

zbMATH Keywords

geometric evolution equationscurves in Euclidean spacedeformable solids

Mathematics Subject Classification ID

Free motion of a rigid body (70E15) Curves in Euclidean and related spaces (53A04) Existence of solutions of dynamical problems in solid mechanics (74H20) Uniqueness of solutions of dynamical problems in solid mechanics (74H25) Strings (74K05) PDEs in connection with mechanics of particles and systems of particles (35Q70)

Cites Work

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• Large buckled states of nonlinearly elastic rods under torsion, thrust, and gravity
• On the dynamics of rods in the theory of Kirchhoff and Clebsch
• Convergence towards an elastica in a Riemannian manifold
• Curve straightening flow deforms closed plane curves with nonzero rotation number to circles
• Hamiltonian dynamics of an elastica and the stability of solitary waves
• Nonlinear dynamical theory of the elastica
• On the Cauchy Problem for a Dynamical Euler's Elastica
• On motion of an elastic wire and singular perturbation of a 1-dimensional plate equation

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