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
Full-text PDF Free Access
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.