Journal of Mathematical Sciences

, Volume 219, Issue 2, pp 208–219 | Cite as

Singular Space-Time Transformations. Towards One Method For Solving the Painlevé Problem

  • B. M. Miller
  • E. Ya. Rubinovich
  • J. Bentsman

We develop the method of singular space-time transformations for systems with impact and friction. We consider a mathematical model of a Painlevé problem concerning impacts of an absolutely rigid bar with a rough surface. Using the method of singular space-time change of variables, we obtain the model of an absolutely rigid body by passing to the limit as the generalized rigidity parameter tends to infinity.


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Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • B. M. Miller
    • 1
  • E. Ya. Rubinovich
    • 2
  • J. Bentsman
    • 3
  1. 1.Institute for Information Transmission Problems of the Russian Academy of SciencesMoscowRussia
  2. 2.V. A. Trapeznikov Institute of Control Sciences of the Russian Academy of SciencesMoscowRussia
  3. 3.University of Illinois at Urbana-ChampaignUrbanaUSA

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