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Regular version of the site

Article

Нелинейная динамика кельтского камня: Неголономная модель

Успехи физических наук. 2014. Т. 184. № 5. С. 493-500.
Казаков А. О., Борисов А. В., Кузнецов С. П.

Based on the results of numerical simulations we discuss and illustrate dynamical phenomena characteristic for the rattleback, a solid body of convex surface moving on a rough horizontal plane, which are associated with the lack of conservation for the phase volume in the nonholonomic mechanical system. Due to local compression of the phase volume, behaviors can be realized, analogous to those occurring in dissipative systems, like stable equilibrium points, corresponding to stationary rotations, limit cycles (rotations with oscillations), strange attractors. A chart of dynamical regimes in the parameter plane of a total mechanical energy and a relative angle between the geometric and dynamic principal axes of the body is plotted and discussed. The transition to chaos through a sequence of Feigenbaum period doubling bifurcations is demonstrated. Several examples of strange attractors are considered; their phase portraits, Lyapunov exponents, and Fourier spectra are discussed.