Spatially complex equilibria of buckled rods

DOI10.1007/BF00251491zbMath0655.73029MaRDI QIDQ1109609

Alexander Mielke, Philip J. Holmes

Publication date: 1988

Published in: Archive for Rational Mechanics and Analysis (Search for Journal in Brave)

zbMATH Keywords

boundary value problemsHamiltonian structureMelnikov functionheteroclinic orbitslimiting casesKirchhoff analogychaotic deformationsexistence of spatially chaotic equilibrium statesgeometrical symmetriesheavy rigid body pivoted at a fixed pointqualitative description of classes of solutionsregular perturbation methodsrod loaded at its endtransverse homoclinicvanishing of certain stress components

Mathematics Subject Classification ID

Rods (beams, columns, shafts, arches, rings, etc.) (74K10) Bifurcation and buckling (74G60) Strange attractors, chaotic dynamics of systems with hyperbolic behavior (37D45)

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Cites Work

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• Large lateral buckling of nonlinearity elastic beams
• Nonlinear oscillations, dynamical systems, and bifurcations of vector fields
• Post-buckling behavior of a nonlinearly hyperelastic thin rod with cross- section invariant under the dihedral group \(D_ n\)
• The Hamiltonian structure of nonlinear elasticity: The material and convective representations of solids, rods, and plates
• Large buckled states of nonlinearly elastic rods under torsion, thrust, and gravity
• Horseshoes in perturbations of Hamiltonian systems with two degrees of freedom
• Differentiable dynamical systems