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Circular orbits of a ball on a rotating conical turntable

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Abstract

This paper is concerned with the problem of a dynamically symmetric heavy ball rolling without slipping on a cone which rotates uniformly about its symmetry axis. The equations of motion of the system are obtained, partial periodic solutions are found, and their stability is analyzed.

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Authors and Affiliations

  1. Moscow Institute of Physics and Technology (State University), Institutskii per. 9, Dolgoprudny, Russia, 141700

    Alexey V. Borisov & Alexander A. Kilin

  2. Udmurt State University, ul. Universitetskaya 1, Izhevsk, Russia, 426034

    Alexey V. Borisov, Tatiana B. Ivanova & Alexander A. Kilin

  3. Kalashnikov Izhevsk State Technical University, ul. Studencheskaya 7, Izhevsk, Russia, 426069

    Ivan S. Mamaev

Authors
  1. Alexey V. Borisov
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  2. Tatiana B. Ivanova
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  3. Alexander A. Kilin
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  4. Ivan S. Mamaev
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Correspondence to Alexey V. Borisov.

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The authors declare that they have no conflict of interest.

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The work of I. S. Mamaev (Sect. 1) was carried out within the framework of the state assignment of the Ministry of Education and Science of Russia (1.2405.2017/4.6). The work of T. B. Ivanova (Sect. 2) was carried out within the framework of the state assignment of the Ministry of Education and Science of Russia (1.2404.2017/4.6). The work of A. V. Borisov and A. A. Kilin (Sects. 3, 4) was carried out at MIPT within the framework of the Project 5-100 for State Support for Leading Universities of the Russian Federation.

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Borisov, A.V., Ivanova, T.B., Kilin, A.A. et al. Circular orbits of a ball on a rotating conical turntable. Acta Mech 231, 1021–1028 (2020). https://doi.org/10.1007/s00707-019-02556-y

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  • DOI: https://doi.org/10.1007/s00707-019-02556-y

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