Large rotating states of a conducting elastic wire in a magnetic field: Subtle symmetry and multiparameter bifurcation

DOI10.1007/BF00115559zbMath0733.73032OpenAlexW2047588276MaRDI QIDQ809672

Timothy J. Healey

Publication date: 1990

Published in: Journal of Elasticity (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf00115559

zbMATH Keywords

invariancelocal analysisgroup-theoretic methodsflexible, nonlinearly elastic, current-carrying wirelarge-amplitude, steadily rotating statesmultiparameter bifurcation problemrotation group SO(2)

Mathematics Subject Classification ID

Nonlinear elasticity (74B20) Crystalline structure (74E15) Electromagnetic effects in solid mechanics (74F15) Symmetric groups (20B30)

Related Items (4)

Buckling of a nonlinearly elastic column: Variational principles, bifurcation and asymptotics ⋮ 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 ⋮ Magnetically-induced buckling of a whirling conducting rod with applications to electrodynamic space tethers

Cites Work

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• A new degree for \(S^ 1\)-invariant gradient mappings and applications
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• Singularities and groups in bifurcation theory. Volume II
• Bifurcation from simple eigenvalues
• Some aspects of nonlinear eigenvalue problems
• Homotopy, linearization, and bifurcation
• Global Bifurcations and Continuation in the Presence of Symmetry with an Application to Solid Mechanics

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