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The model of a mechanical system subjected to unilateral constraints, together with the model of stability based on the Aizerman–Gantmakher theory, are presented. Some examples of numerical computation of Lyapunov exponents for the system of triple physical pendulum with the horizontal barrier, using presented model of stability, are reported.
Using an effective algorithm based on analysis of the wandering trajectories, chaotic behavior regions of oscillators with hysteresis are obtained in various parametric planes. Substantial influence of a hysteretic dissipation value on the form and location of these regions and also restraining and generating effects of the hysteretic dissipation on a chaos occurrence are demonstrated.
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