Equilibrium States of an Elastic Conductor in a Magnetic Field: A Paradigm of Bifurcation Theory

DOI10.2307/1999323zbMath0519.73093OpenAlexW4252371476MaRDI QIDQ3669008

Peter Wolfe

Publication date: 1983

Full work available at URL: https://doi.org/10.2307/1999323

zbMATH Keywords

magnetic fieldequilibrium statesconstant magnetic fieldelectric currentsolved exactlyperfectly flexiblesuspended between fixed supportsbranches of nontrivial solutions obtained at eigenvalues of equilibrium equation linearized about trivial solutiondirection parallel to line between supportsnonlinearly elastic conducting wireparadigmatic bifurcation diagramstability of various solution branchesstate of tension

Mathematics Subject Classification ID

Bifurcation and buckling (74G60) Electromagnetic effects in solid mechanics (74F15) Bifurcations in context of PDEs (35B32) Electro- and magnetostatics (78A30)

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Equilibrium states of an elastic conducting rod in a magnetic field ⋮ Nonlinear stability analysis of a clamped rod carrying electric current ⋮ Nonlinear dynamics and snap-through regimes of a bistable buckled beam excited by an electromagnetic Laplace force ⋮ Bifurcation theory of an elastic conducting wire subject to magnetic forces ⋮ A few results on the foundation of the theory and behavior of nonlinear magnetoelastic plates carrying an electrical current ⋮ Magnetically-induced buckling of a whirling conducting rod with applications to electrodynamic space tethers ⋮ Homoclinic complexity in the localised buckling of an extensible conducting rod in a uniform magnetic field ⋮ A new degree for \(S^ 1\)-invariant gradient mappings and applications

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