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IssuesArchive of Issues2021-3pp.349-367

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Rosenblat G.M., "On the balance of an inextensible heavy thread on a cone or sphere," Mech. Solids. 56 (3), 349-367 (2021)
Year 2021 Volume 56 Number 3 Pages 349-367
DOI 10.3103/S0025654421030092
Title On the balance of an inextensible heavy thread on a cone or sphere
Author(s) Rosenblat G.M. (Moscow State Automobile and Road Technical University, Moscow, 125319 Russia, gr51@mail.ru)
Abstract The problem of finding equilibrium configurations of a heavy inextensible closed thread (chain) on a smooth surface is considered. The surface is a one-way bond for the thread and is either a circular cone, the axis of which is parallel to the vertical (gravity), or a sphere. It is shown: 1) for a cone, equilibrium non-horizontal configurations of a thread-chain are possible only when the opening angle of the cone is within the range from 60 to 90 degrees; 2) for a sphere, equilibrium non-horizontal configurations of a thread-chain are impossible.
Keywords flexible inextensible thread, equilibrium, cone, sphere, elliptic integral of the third kind
Received 31 August 2020Revised 01 September 2020Accepted 02 September 2020
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