CHAOS IN PIECEWISELY INTEGRABLE TRAIN MODEL FOR TWO BLOCKS

J. Szkutnik and K. Kułakowski ()
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J. Szkutnik: Faculty of Physics and Nuclear Techniques, University of Mining and Metallurgy, al. Mickiewicza 30, 30-059 Kraków, Poland
K. Kułakowski: Faculty of Physics and Nuclear Techniques, University of Mining and Metallurgy, al. Mickiewicza 30, 30-059 Kraków, Poland

International Journal of Modern Physics C (IJMPC), 2002, vol. 13, issue 01, 41-48

Abstract: The train model of two blocks with stick-slip dynamics (M. de Sousa Vieira, 1995) is believed to be the simplest spring-block system, which displays chaos. Here we simplify it even more by linearizing the velocity dependence of the friction force. In this way, the nonlinearity of the equations of motion is reduced to the time moments, when a block starts to move or stops, and when the analytical solutions are to be sewn together. We demonstrate, that for small values of the velocity of blocks, the character of motion is not changed. This is observed on the bifurcation diagrams, the Lyapunov exponents, the phase portraits and the power spectra.

Keywords: Low-dimensional; chaos (search for similar items in EconPapers)
Date: 2002
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DOI: 10.1142/S0129183102002924

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