This paper examines the oscillations of a spherical pendulum with horizontal Lissajous excitation. The pendulum has two degrees of freedom: a rotational angle defined in the horizontal plane and an inclination angle defined by the pendulum with respect to the vertical z axis. The results of numerical simulations are illustrated with the mathematical model in the form of multi-colored maps of the largest Lyapunov exponent. The graphical images of geometrical structures of the attractors placed on Poincaré cross sections are shown against the maps of the resolution density of the trajectory points passing through a control plane. Drawn for a steady-state, the graphical images of the trajectory of a tip mass are shown in a three-dimensional space. The obtained trajectories of the moving tip mass are referred to a constructed bifurcation diagram.

We examine the nonlinear response of two planar pendula under external and kinematic excitations, which are very relevant as paradigmatic models in nonlinear dynamics. These pendula act under the action of an additional constant torque, and are subjected to one of the following excitations: a further external periodic torque, and a vertically periodic forcing of the point of suspension. Here, we show the influence of the constant torque strength on the transition to chaotic motions of the pendulum using both Melnikov analysis and the computation of the basins of attraction. The global bifurcations are illustrated by the erosion of the corresponding basins of attraction.

We use friction to simultaneously damp and excite a pendulum system. A Froude pendulum attached to a suspension shaft is subjected to a frictional load. We investigate two types of response of the system: regular and chaotic responses, depending on the excitation frequency. A transient chaotic solution was also obtained. We identify the motions using phase portraits, Poincaré maps, and Fourier spectra. Finally, the composite multiscaled entropy was estimated for the specified cases to confirm the preliminary classification.

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This article is the result of my research on the authorities of the People’s Republic of Poland (PRL). During my study, I used the methodology of sociological qualitative research, specifically the biographical method, to investigate the operating mechanisms of the authorities of the PRL. I based the article on recorded interviews with 32 former members of the Security Service (SB) apparatus, as well as other biographical materials contained in the personal files of SS (SB) officers. While analysing them, I referred to research on the totalitarian system, in particular a paper on the subject of the history, structure and activities of the SS (SB). The aim of this article is to present the phenomenon of hidden religiosity among SS (SB) functionaries, which led to team loyalty resulting from knowledge of reciprocal offenses and the possibility of blackmail. Adam Podgórecki named this a „dirty community”.