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Numerical Analysis of Shock Interactions with the Example of Painleve Paradox with a “Slanted” Fall of a Rod

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Abstract

We consider a system that belongs to the class of well-known Painlevé problems; to solve it, we use the method of opening spatio-temporal singularities proposed by the authors. This method makes it possible to unambiguously solve the problem of finding the speeds of a body after hitting a surface with dry friction, i.e., to resolve a situation where traditional approaches either yield an ambiguous answer or lead to an infeasible system of relations (the Painlevé paradox).

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Acknowledgements

This work was supported in part by the Russian Foundation for Basic Research, projects nos. 16-08-01285 and 16-08-01076.

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Authors and Affiliations

  1. Kharkevich Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, Russia

    B. M. Miller

  2. Monash University, Melbourne, Victoria, Australia

    B. M. Miller

  3. Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia

    E. Ya. Rubinovich

Authors
  1. B. M. Miller
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  2. E. Ya. Rubinovich
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Correspondence to B. M. Miller.

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Russian Text © The Author(s), 2019, published in Avtomatika i Telemekhanika, 2019, No. 10, pp. 100–114.

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Miller, B.M., Rubinovich, E.Y. Numerical Analysis of Shock Interactions with the Example of Painleve Paradox with a “Slanted” Fall of a Rod. Autom Remote Control 80, 1835–1846 (2019). https://doi.org/10.1134/S0005117919100059

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