Journal of Elasticity

, Volume 24, Issue 1–3, pp 211–227 | Cite as

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

  • Timothy J. Healey
Article

Abstract

In this paper we consider large-amplitude, steadily rotating states of a flexible, nonlinearly elastic, current-carrying wire in a magnetic field. Our formulation leads naturally to a multiparameter bifurcation problem. A detailed local analysis is ostensibly intractable, due to the presence of the rotation group SO(2). However, we identify an additional, more subtle symmetry, which enables a standard local bifurcation analysis via group-theoretic methods. In contrast to well known methods of local equivariant bifurcation theory, we first exploit the group invariance of the full problem (before performing a local reduction) to construct a reduced problem that is also amenable to a global analysis, which we provide.

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Copyright information

© Kluwer Academic Publishers 1990

Authors and Affiliations

  • Timothy J. Healey
    • 1
    • 2
  1. 1.Department of Theoretical & Applied MechanicsCornell UniversityIthacaU.S.A.
  2. 2.Center for Applied MathematicsCornell UniversityIthacaU.S.A.

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