Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Equilibria of the circular elastica under a uniform central force field

Authors: R. W. Dickey and J. J. Roseman
Journal: Quart. Appl. Math. 51 (1993), 201-216
MSC: Primary 73H05
DOI: https://doi.org/10.1090/qam/1218364
MathSciNet review: MR1218364
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Abstract: A mathematical model for the problem of an inextensible circular elastica under a uniform centrally directed force field is derived and studied. It is shown analytically that stable large amplitude solutions exist at forces $ P < {P_1}$, the first eigenpressure for the linearized model, and it is shown numerically that these solutions have only one axis of symmetry. These results agree with experiment. In addition, numerical solutions are calculated for states with more than one axis of symmetry which resemble those found in the literature on elastic rings under hydrostatic pressure.

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DOI: https://doi.org/10.1090/qam/1218364
Article copyright: © Copyright 1993 American Mathematical Society

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