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Bifurcation theory of an elastic conducting wire subject to magnetic forces

โœ Scribed by Peter Wolfe

Book ID
104624009
Publisher
Springer Netherlands
Year
1990
Tongue
English
Weight
597 KB
Volume
23
Category
Article
ISSN
0374-3535

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โœฆ Synopsis

In this paper we study the equilibrium states of a nonlineafly elastic wire in a magnetic field. The wire is perfectly flexible, is suspended between fixed supports and carries an electric current. We consider two problems. The first in which the magnetic field is constant can be solved exactly. The set of solutions illustrates the phenomenon of "symmetry breaking" which is a chapter in the theory of imperfect bifurcation. The second problem is one in which the magnetic field is produced by current flowing in a pair of infinitely long parallel wires. When the line of supports of the elastic wire is parallel to these and equidistant from them we may apply the global bifurcation results of Crandall and Rabinowitz to study the set of solutions. We also consider perturbations of this case. This is another example of imperfect bifurcation.

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โœ Timothy J. Healey ๐Ÿ“‚ Article ๐Ÿ“… 1990 ๐Ÿ› Springer Netherlands ๐ŸŒ English โš– 652 KB

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