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- W2038565425 abstract "The problem to be considered here is the determination of the possible configurations of a perfectly flexible and inextensible heavy chain rotating uniformly about an axis in the direction of the gravitational acceleration and with both ends fixed, a given distance apart, to the axis of rotation. This problem has recently become of interest in connection with the design of vertical axis wind turbines’ and is also of importance in the study of rotating threads in the spinning industry.2 In spite of comprehensive analyses and sophisticated treatments of this problem in three modern papers2-4 no one has yet succeeded in proposing a method, analytical or numerical, which gives a quantitative description of the configurations of heavy rotating chains. Since the chain may assume nodes on the vertical axis between the two fixed ends more than one possible nodal configuration must be allowed for, given a particular angular velocity of rotation. In this paper we present a simple numerical method by which, through physical discretization of the chain, the different nodal configurations may easily be calculated for any given angular velocity. In addition, in agreement with the work of Kolodner,3 the existence of a critical angular velocity for each nodal configuration, below which it cannot exist, is also demonstrated. To illustrate the basic difference between the conventional approach to the problem and ours we consider first, very briefly, the essentials of the continuous formulation as set out in the definitive article of Kolodner3 and as used by subsequent authors.2,4" @default.
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- W2038565425 date "1979-06-01" @default.
- W2038565425 modified "2023-09-25" @default.
- W2038565425 title "Numerical determination of the configurations of heavy rotating chains" @default.
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- W2038565425 doi "https://doi.org/10.1016/0307-904x(79)90056-8" @default.
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