Equilibrium states of an elastic conductor in a magnetic field: a paradigm of bifurcation theory
Peter Wolfe
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Source: Crossref
Published: Jan 1, 1983
DOI: 10.1090/s0002-9947-1983-0697082-3
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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.
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