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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Equilibrium states of an elastic conductor in a magnetic field: a paradigm of bifurcation theory
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by Peter Wolfe PDF
Trans. Amer. Math. Soc. 278 (1983), 377-387 Request permission

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
    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
  • © Copyright 1983 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 278 (1983), 377-387
  • MSC: Primary 73R05; Secondary 58E07, 73C50
  • DOI: https://doi.org/10.1090/S0002-9947-1983-0697082-3
  • MathSciNet review: 697082