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The stability of a top rotating on a rough horizontal plane

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Abstract

In the present paper the stability of permanent rotation of a symmetric top rotating on a slightly rough horizontal plane about the erect polar or transverse axis is discussed via the perturbation method. As a perturbation factor, the frictional force is an arbitrary nonlinear function of the sliding velocity. The same stability criterion as that in the Contensou-Magnus linear theory is obtained, but the hypothesis of the linearity for friction can be omitted. It shows that the direction of the sliding velocity at the contact point is an important factor, which influences the stability of the top. And then an explicit physical explanation is given.

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Authors and Affiliations

  1. Department of Engineering Mechanics, Shanghai Jiao Tong University, Shanghai, China

    Liu Yanzhu

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  1. Liu Yanzhu
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Yanzhu, L. The stability of a top rotating on a rough horizontal plane. Acta Mech Sinica 3, 278–285 (1987). https://doi.org/10.1007/BF02486774

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  • DOI: https://doi.org/10.1007/BF02486774

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