Equilibrium states of an elastic conductor in a magnetic field: a paradigm of bifurcation theory
Trans. Amer. Math. Soc. 278 (1983), 377-387
Primary 73R05; Secondary 58E07, 73C50
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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.
F. C. Moon, Problems in magneto-solid mechanics, Mechanics Today, Vol 4 (Nemat-Nasser, editor), Pergamon Press, Oxford, 1978.
- F. C. Moon, Problems in magneto-solid mechanics, Mechanics Today, Vol 4 (Nemat-Nasser, editor), Pergamon Press, Oxford, 1978.
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