Related papers: Extreme rotational events in a forced-damped nonli…
The fundamental mode of rotation in quantum fluids is given by a vortex, whose quantized value yields the orbital angular momentum (OAM) per particle. If the vortex is displaced (off-centered) from the reference point for rotation, the…
Using the damped pendulum system we introduce the averaging method to study the periodic solutions of a dynamical system with small perturbation. We provide sufficient conditions for the existence of periodic solutions with small amplitude…
The effects of large scale mechanical forcing on the dynamics of rotating turbulent flows are studied by means of numerical simulations, varying systematically the nature of the mechanical force in time. We demonstrate that the…
We describe a mechanism for transport of energy in a mechanical system consisting of a pendulum and a rotator subject to a random perturbation. The perturbation that we consider is the product of a Hamiltonian vector field and a scalar,…
Intermittent large amplitude events are seen in the temporal evolution of a state variable of many dynamical systems. Such intermittent large events suddenly start appearing in dynamical systems at a critical value of a system parameter and…
This paper is concerned with the analysis of a class of impacting systems of relevance in applications: cam-follower systems. We show that these systems, which can be modelled as discontinuously forced impact oscillators, can exhibit…
We investigate the hopping dynamics between different attractors in a multistable system under the influence of noise. Using symbolic dynamics we find a sudden increase of dynamical entropies, when a system parameter is varied. This effect…
Time-delayed control in a balancing problem may be a nonsmooth function for a variety of reasons. In this paper we study a simple model of the control of an inverted pendulum by either a connected movable cart or an applied torque for which…
This paper is devoted to a detailed investigation of the perturbed pendulum-like motions of a heavy rigid body about a fixed point. Canonical variables that allow one to simplify the analysis of homoclinic and heteroclinic orbits are…
The motion of a large, neutrally buoyant, particle, freely advected by a turbulent flow is determined experimentally. We demonstrate that both the translational and angular accelerations exhibit very wide probability distributions, a…
Chaos in classical systems has been studied in plenty over many years. Although the search for chaos in quantum systems has been an area of prominent research over the last few decades, the detailed analysis of many inherently chaotic…
This paper extends our previous work~(Szumi\'nski and Maciejewski, 2024), where we explored the dynamics and integrability of the double-spring pendulum. Here, we investigate the variable-length double pendulum, a three-degree-of-freedom…
Diffusion is a fundamental aspect of transport processes in biological systems, and thus, in the development of life itself. And yet, the diffusive dynamics of active fluids with directed rotation, known as chiral fluids, has not been…
The single, double, and triple pendulum has served as an illustrative experimental benchmark system for scientists to study dynamical behavior for more than four centuries. The pendulum system exhibits a wide range of interesting behaviors,…
The dynamics of driven, damped pendulum as used in mechanical clocks is numerically investigated. In addition to the analysis of a well-known mechanisms such as chronometer escapement, the unusual properties of Harrison's grasshopper…
Extreme events are ubiquitous in a wide range of dynamical systems, including turbulent fluid flows, nonlinear waves, large scale networks and biological systems. Here, we propose a variational framework for probing conditions that trigger…
The looping pendulum is a simple physical system consisting of two masses connected by a string that passes over a rod. We derive equations of motion for the looping pendulum using Newtonian mechanics, and show that these equations can be…
Frequency responses of multi-degree-of-freedom mechanical systems with weak forcing and damping can be studied as perturbations from their conservative limit. Specifically, recent results show how bifurcations near resonances can be…
Non-linear dynamics is not a usually covered topic in undergraduate physics courses. However, its importance within classical mechanics and the general theory of dynamical systems is unquestionable. In this work we show that this subject…
In this work we investigate, by means of direct numerical simulations, how rotation affects the bi-dimensionalization of a turbulent flow. We study a thin layer of fluid, forced by a two-dimensional forcing, within the framework of the…