Grzegorz Wasilewski

In this work, we analyzed theoretically and experimentally the nonlinear dynamics of a magnetic pendulum driven by a coil-magnet interaction. The force between the magnetic elements and the resulting torque on the pendulum are derived using both the magnetic charges interaction model and the experimentally fitted interaction model. This enables the comparison between the two models. The current in the coil is taken first as a sinusoidal current and then as a square current. The comparison of the structure of each interaction model is conducted and it appears that they give qualitatively similar characteristics. The harmonic balance method is used to approximate the frequency responses of the pendulum leading to both symmetric and asymmetric or one-side (intrawell) oscillations. The two-parameters bifurcation diagrams are plotted showing the different dynamical behaviors considering the current amplitude and frequency as the control parameters. Good agreements are found between our theoretical results and experimental ones.

Impacting mechanical systems with suitable parameter settings exhibit a large amplitude chaotic oscillation close to the grazing with the impacting surface. The cause behind this uncertainty is the square root singularity and the occurrence of dangerous border collision bifurcation. In the case of one-degree-of-freedom mechanical systems, it has already been shown that this phenomenon occurs under certain conditions. This paper proposes the same uncertainty of a two-degree freedom mechanical impacting system under specific requirements. This paper shows that the phenomena earlier reported in the case of one-degree-of-freedom mechanical systems (like narrow band chaos, finger-shaped attractor, etc.) also occur in the two-degrees-of-freedom mechanical impacting system. We have numerically predicted that the narrowband chaos ensues under specific parameter settings. We have also shown that narrowband chaos can be avoided under some parameter settings. At last, we demonstrate the numerical predictions experimentally by constructing an equivalent electronic circuit of the mechanical rig.

Impacting mechanical systems with suitable parameter settings exhibit a large amplitude chaotic oscillation close to the grazing with the impacting surface. The cause behind this uncertainty is the square root singularity and the occurrence of dangerous border collision bifurcation. In the case of one degree of freedom mechanical systems, it has already been shown that this phenomenon occurs under certain conditions. This paper proposes the same uncertainty of a two-degree freedom mechanical impacting system under specific requirements. This paper shows that the phenomena earlier reported in the case of one degree of freedom mechanical systems (like narrow band chaos, finger-shaped attractor, etc.) also occur in the two degrees of freedom mechanical impacting system. We have numerically predicted the narrowband chaos ensues under specific parameter settings. We have also shown that the narrowband chaos can be avoided under some parameter settings. At last, we demonstrate the numerical predictions experimentally by constructing an equivalent electronic circuit of the mechanical rig.

The paper deals with the studies of forced impacting oscillator when are taken into account the dry and viscous resistance, as well as the generalized Hertz contact law during an impact. The numerical treatments of mathematical model are accompanied with the validations on the base of experimental rig. To study the solutions of the mathematical model, we construct the sequences of impacts, when the system is evolved in periodic and chaotic modes. The statistical properties of chaotic impact events are considered in more details. In particular, we analyze the successive iterations of impact map, autocorrelation function and coefficient of variation for the impact train, the histograms for the inter-impact intervals and values of obstacle penetrations. It is revealed that the impact sequence is stationary but non-Poissonian and contains temporal scales which do not relate to the external stimulus. This sequence can be described by a bimodal distribution. These findings are confirmed by the analysis of experimental data.

A mathematical model of a system consisting of a dc motor, mechanism converting the rotational motion to the linear one and a single physical pendulum with the joint horizontally driven is developed. Constant angular velocity of the crank is assumed. The parameters of the model are estimated using the experimental data consisting of five solutions corresponding to the five different values of constant input voltage. Different versions of the mathematical model, with different details concerning friction and damping modelling, are tested. A good agreement between real and simulated behaviour of the system is obtained. Moreover the model is validated by testing its ability to predict critical values of the bifurcation parameter.

Experimental results with swinging up a double pendulum using a bang-bang control torque exerted about the suspension point are presented. In the course of the experiment, the feedback control brings...