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- W2073243368 abstract "This paper treats the steady motion under gravity of both inextensible and elastic strings that are simultaneously whirled and drawn. The motion is governed by a quasilinear system of singular ordinary differential equations that depend on the two parameters $omega $ and $gamma $, which are the rates of whirling and drawing. The singular nonlinear problem is approximated by a sequence of regular problems to which global multiparameter bifurcation theory is applied. It is then shown that the sequence of solution sheets for the approximating problems converges to solution sheets of the actual problem. All these solution sheets, infinite in number, are shown to bifurcate from the $omega $- and $gamma $-axes, which form the boundaries of the continuous spectra for the problem linearized about the trivial solution. (These linearized problems have no eigenvalues.) Nevertheless, each bifurcating sheet is characterized by a novel and distinctive nodal pattern. The nature of steady shocks in elastic strings is briefly discussed." @default.
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- W2073243368 date "1987-03-01" @default.
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- W2073243368 title "The Drawing and Whirling of Strings: Singular Global Multiparameter Bifurcation Problems" @default.
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- W2073243368 doi "https://doi.org/10.1137/0518027" @default.
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