 | | Mechanics of Solids
A Journal of Russian Academy of Sciences | | Founded
in January 1966
Issued 6 times a year
Print ISSN 0025-6544
Online ISSN 1934-7936 |
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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 |
| Link to Fulltext |
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