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On the topological structure of the set of generalized solutions of the catenary problem

Published online by Cambridge University Press:  14 November 2011

J. C. Alexander  and
Michael Reeken
J. C. Alexander
Affiliation:
Department of Mathematics, University of Maryland, College Park, MD 20742, U.S.A.
Michael Reeken
Affiliation:
Fachbereich Mathematik, Bergische Universität-Gesamthochschule Wuppertal, Gaußstraße 20, D-5600 Wuppertal 1, Federal Republic of Germany
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Synopsis

The global topological structure of the space of configurations of a non-rotating elastic string under compression and tension is studied. The part of the string under tension is specified by a measurable subset of the interval. The set of such intervals, with the Hausdorff topology, is considered a parameter space for the equation satisfied by the string, and the solutions are shown to form an infinitedimensional continuum over this parameter space. A new global topological theorem is needed, since the parameter space is not Euclidean. The topological theorem is based on the fixed-point transfer.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 98 , Issue 3-4 , 1984 , pp. 339 - 348
Copyright
Copyright © Royal Society of Edinburgh 1984

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References

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