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Discontinuity-induced bifurcations of a dual-point contact ball

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Abstract

In this paper, dynamics of a ball is investigated, which is in dual-point contact with a cylindrical vessel. This model is based on a concept of a type of flowmeter. Rolling, slipping and separation of surfaces can all occur at both contact points, which results in a nonsmooth dynamical system. Stationary solutions of the system and their stability are determined in the different kinematic cases. By introducing the concept of stability with respect to slipping, existence of the stationary solutions can be checked even in the case when the contact forces are undetermined. Discontinuity-induced bifurcations of the system are explored.

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Acknowledgments

The research leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP/2007-2013)/ERC Advanced Grant Agreement No. 340889. We thank Csaba Hos of the University of Technology and Economics for the useful comments. We thank the reviewers for the useful critical comments and suggestions.

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Authors and Affiliations

  1. Department of Applied Mechanics, Budapest University of Technology and Economics, Budapest, 1521, Hungary

    Mate Antali & Gabor Stepan

  2. HAS-BME Research Group on Dynamics of Machines and Vehicles, Hungarian Academy of Sciences, Budapest, 1521, Hungary

    Gabor Stepan

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  1. Mate Antali
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  2. Gabor Stepan
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Correspondence to Mate Antali.

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Antali, M., Stepan, G. Discontinuity-induced bifurcations of a dual-point contact ball. Nonlinear Dyn 83, 685–702 (2016). https://doi.org/10.1007/s11071-015-2356-y

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