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IssuesArchive of Issues2010-1pp.27-33

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V.P. Legeza, "Brachistochrone for a Rolling Cylinder," Mech. Solids. 45 (1), 27-33 (2010)
Year 2010 Volume 45 Number 1 Pages 27-33
DOI 10.3103/S002565441001005X
Title Brachistochrone for a Rolling Cylinder
Author(s) V.P. Legeza (National University of Food Technologies, Vladimirskaya 68, Kiev, 01601 Ukraine, Viktor_Legeza@ukr.net)
Abstract The motion of a heavy homogeneous cylinder is considered as a no-slip rolling along the desired curve. We obtain a functional in the form of the total time of the cylinder rolling and solve the corresponding variational problem of minimizing this functional. We obtain an algebraic equation for the directional line of steepest descent, brachistochrone, in parametric form. We use the equation of motion of the cylinder with constraint reaction to determine the conditions of implementation of its pure rolling without separation and slip with respect to the brachistochrone.
Keywords brachistochrone, cylinder rolling without slip, variational problem, functional minimization, cycloid, Euler-Poisson equation
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Received 17 January 2008
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