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Motion of a cylinder on a circularly vibrating horizontal rough plane with an arbitrary law of normal tensions

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Abstract

The motion of a uniform dynamically symmetric cylindrical body (washer, cylinder) on a horizontal rough plane, which performs a specified translatory circular periodic motion, is considered. It is shown that all motions of the cylinder, if the distribution laws of normal tensions are admissible and the condition of tilting absence is fulfilled, tend to the established motion in which the cylinder moves in a translator manner (its angular velocity equals zero) in the system of coordinates rigidly connected with a mobile support plane, while its center of mass moves with a constant velocity along the circle. This motion is the sole one and is asymptotically stable (in the space of velocities). Thus, the established motion of the body is here similar to the result by Zhukowski found for a material point.

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Authors and Affiliations

  1. Moscow State Automobile and Road Technical University (MADI), Leningradskii pr. 64, Moscow, 125319, Russia

    G. M. Rozenblat

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  1. G. M. Rozenblat
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Correspondence to G. M. Rozenblat.

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Original Russian Text © G.M. Rozenblat, 2015, published in Doklady Akademii Nauk, 2015, Vol. 460, No. 2, pp. 159–164.

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Rozenblat, G.M. Motion of a cylinder on a circularly vibrating horizontal rough plane with an arbitrary law of normal tensions. Dokl. Phys. 60, 28–33 (2015). https://doi.org/10.1134/S1028335815010061

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  • DOI: https://doi.org/10.1134/S1028335815010061

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