Brachistochrone for a rolling cylinder |
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Authors: | V P Legeza |
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Institution: | 1.National University of Food Technologies,Kiev,Ukraine |
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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. |
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Keywords: | |
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