, Volume 24, Issue 1-3, pp 211-227

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

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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.

Supported in part by the U.S. Army Research Office through the Mathematical Sciences Institute of Cornell University, Contract DAAG29-85-C-0018, and by the Air Force Office of Scientific Research, Grant No. AFOSR-88-0222.