Large rotating states of a conducting elastic wire in a magnetic field: subtle symmetry and multiparameter bifurcation
- Timothy J. Healey
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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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- Large rotating states of a conducting elastic wire in a magnetic field: subtle symmetry and multiparameter bifurcation
Journal of Elasticity
Volume 24, Issue 1-3 , pp 211-227
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- Kluwer Academic Publishers
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- Timothy J. Healey (1) (2)
- Author Affiliations
- 1. Department of Theoretical & Applied Mechanics, Cornell University, 14850, Ithaca, NY, U.S.A.
- 2. Center for Applied Mathematics, Cornell University, 14850, Ithaca, NY, U.S.A.