Large rotating states of a conducting elastic wire in a magnetic field: subtle symmetry and multiparameter bifurcation
✍ Scribed by Timothy J. Healey
- Publisher
- Springer Netherlands
- Year
- 1990
- Tongue
- English
- Weight
- 652 KB
- Volume
- 24
- Category
- Article
- ISSN
- 0374-3535
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✦ Synopsis
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.