ABSTRACT
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ABSTRACT
In this paper we show the first broad experimental confirmation of the basin stability approach. The basin stability is one of the sample-based approach methods for analysis of the complex, multidimensional dynamical systems. We show that investigated method is a reliable tool for the analysis of dynamical systems and we prove that it has a significant advantages which make it appropriate for many applications in which classical analysis methods are difficult to apply. We study theoretically and experimentally the dynamics of a forced double pendulum. We examine the ranges of stability for nine different solutions of the system in a two parameter space, namely the amplitude and the frequency of excitation. We apply the path-following and the extended basin stability methods (Brzeski et al., Meccanica 51(11), 2016) and we verify obtained theoretical results in experimental investigations. Comparison of the presented results show that the sample-based approach offers comparable precision to the classical method of analysis. However, it is much simpler to apply and can be used despite the type of dynamical system and its dimensions. Moreover, the sample-based approach has some unique advantages and can be applied without the precise knowledge of parameter values.
ABSTRACT
We study the occurrence of the synchronous rotation of a set of four uncoupled nonidentical double pendula arranged into a cross structure mounted on a vertically excited platform. Under the excitation, the pendula can rotate in different directions (counter-clockwise or clockwise). It has been shown that after a transient, many different types of synchronous configurations with the constant phase difference between pendula can be observed. The experimental results qualitatively agree with the numerical simulations.
