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


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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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B. Miller

Institute for Information Transmission Problems of the Russian Academy of Sciences

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Email: bmiller@iitp.ru
俄罗斯联邦, 19, Bol’shoi Karetnyi per., Moscow, 127051

E. Rubinovich

V. A. Trapeznikov Institute of Control Sciences of the Russian Academy of Sciences

Email: bmiller@iitp.ru
俄罗斯联邦, 65, Profsoyuznaya St., Moscow, 117997

J. Bentsman

University of Illinois at Urbana-Champaign

Email: bmiller@iitp.ru
美国, 1206 W. Green St., Urbana, IL, 61801

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