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Study of a transition in the qualitative behavior of a simple oscillator with Coulomb friction

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Abstract

A simple mass-spring system is submitted to a constant force in addition to a periodic perturbation of rectangular wave shape. It has been obtained in a previous study that the range of the period-amplitude plane of this perturbation, where the trajectories are sliding with no loss of contact, is divided into two parts, one in which there exist infinitely many equilibrium states and no periodic solutions, and another one where there exist periodic solutions and no equilibrium states. The present work focuses on the transition between these two parts. All along the transition line, there exists a single equilibrium state. Initial data out of equilibrium lead either to a periodic trajectory, or to a trajectory, which tends to the equilibrium or to a periodic solution, either in finite time or at infinity.

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Authors and Affiliations

  1. Laboratoire de Mécanique et d’Acoustique, CNRS, 31, Chemin Joseph Aiguier, 13402, Marseille Cedex 20, France

    Elaine Pratt & Alain Léger

  2. Department of Mathematics and MOE-LSC, Shanghai Jiao Tong University, Minhang Campus, Shanghai, 200240, China

    Xiang Zhang

Authors
  1. Elaine Pratt
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  2. Alain Léger
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  3. Xiang Zhang
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Correspondence to Elaine Pratt.

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Pratt, E., Léger, A. & Zhang, X. Study of a transition in the qualitative behavior of a simple oscillator with Coulomb friction. Nonlinear Dyn 74, 517–531 (2013). https://doi.org/10.1007/s11071-013-0985-6

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  • DOI: https://doi.org/10.1007/s11071-013-0985-6

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