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Chattering as a singular problem

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Abstract

This paper presents the chattering through the singularity point of view for the first time. The main novelty of this article is that impact moments are considered as a singularity phenomenon. A bouncing ball, an inverted pendulum and a hydraulic relief valve models are considered for the study. Moreover, the behavior of solutions of a spring-mass system is studied for the small mass. Simulations are given to support the theoretical analysis.

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Acknowledgements

The authors wish to express their sincere gratitude to the associated editor and the referees for the helpful criticism and valuable suggestions, which helped to improve the paper significantly.

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Authors and Affiliations

  1. Department of Mathematics, Middle East Technical University, 06800, Ankara, Turkey

    Marat Akhmet & Sabahattin Çağ

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  1. Marat Akhmet
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  2. Sabahattin Çağ
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Correspondence to Marat Akhmet.

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Akhmet, M., Çağ, S. Chattering as a singular problem. Nonlinear Dyn 90, 2797–2812 (2017). https://doi.org/10.1007/s11071-017-3840-3

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