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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Equilibrium states of an elastic conductor in a magnetic field: a paradigm of bifurcation theory


Author: Peter Wolfe
Journal: Trans. Amer. Math. Soc. 278 (1983), 377-387
MSC: Primary 73R05; Secondary 58E07, 73C50
MathSciNet review: 697082
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Abstract: In this paper we study the equilibrium states of a nonlinearly elastic conducting wire in a magnetic field. The wire is perfectly flexible and is suspended between fixed supports. The wire carries an electric current and is subjected to a constant magnetic field whose direction is parallel to the line between the supports. We solve this problem exactly and show that the set of solutions gives rise to a paradigmatic bifurcation diagram. We then carry out a study of the equations obtained by linearization about the nontrivial solutions in order to gain some insight into the stability of the various solution branches.


References [Enhancements On Off] (What's this?)

  • [1] F. C. Moon, Problems in magneto-solid mechanics, Mechanics Today, Vol 4 (Nemat-Nasser, editor), Pergamon Press, Oxford, 1978.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9947-1983-0697082-3
PII: S 0002-9947(1983)0697082-3
Article copyright: © Copyright 1983 American Mathematical Society