Related papers: Parametric resonance and nonlinear dynamics in a c…
We investigate the classical problem of motion of a mathematical pendulum with an oscillating pivot. This simple mechanical setting is frequently used as the prime example of a system exhibiting the parametric resonance phenomenon, which…
The stationary and highly non-stationary resonant dynamics of the harmonically forced pendulum are described in the framework of a semi-inverse procedure combined with the Limiting Phase Trajectory concept. This procedure, implying only…
The problem of the effect of two-frequency quasi-periodic perturbations on systems close to arbitrary nonlinear two-dimensional Hamiltonian ones is studied in the case when the corresponding perturbed autonomous systems have a double limit…
The quantum mechanical equivalent of parametric resonance is studied. A simple model of a periodically kicked harmonic oscillator is introduced which can be solved exactly. Classically stable and unstable regions in parameter space are…
In this paper we apply the method of Lagrangian descriptors as an indicator to study the chaotic and regular behavior of trajectories in the phase space of the classical double pendulum system. In order to successfully quantify the degree…
In this work, we study a mathematical planar pendulum whose support point is positioned equidistant between two vertical and uniformly electrically charged wires. Its bob carries an electric charge and, its support point oscillates…
We study in this paper the behavior of a periodically driven nonlinear mechanical system. Bifurcation diagrams are found which locate regions of quasiperiodic, periodic and chaotic behavior within the parameter space of the system. We also…
We present an analytical description of the large-amplitude stationary oscillations of the finite discrete system of harmonically-coupled pendulums without any restrictions to their amplitudes (excluding a vicinity of $\pi$). Although this…
This article describes a numerical procedure designed to tune the parameters of periodically-driven dynamical systems to a state in which they exhibit rich dynamical behavior. This is achieved by maximizing the diversity of subharmonic…
We focus our attention on some relevant aspects of the beam-plasma instability in order to refine some features of the linear and non-linear dynamics. After a re-analysis of the Poisson equation and of the assumption dealing with the…
Much of the physical world around us can be described in terms of harmonic oscillators in thermodynamic equilibrium. At the same time, the far from equilibrium behavior of oscillators is important in many aspects of modern physics. Here, we…
Dynamically stable periodic rotations of a driven pendulum provide a unique mechanism for generating a uniform rotation from bounded excitations. This paper studies the effects of a small ellipticity of the driving, perturbing the classical…
Locally resonant metamaterials are among the most studied types of elastic/acoustic metamaterials, with significant research focused on wave propagation in a continuum of "meta-atoms" Here we investigate the collision dynamics of two…
The resonances of forced dynamical systems occur when either the amplitude of the frequency response undergoes a local maximum (amplitude resonance) or phase lag quadrature takes places (phase resonance). This study focuses on the phase…
We consider systems characterized by the presence of a rapidly oscillating force. A general method is presented for the construction of the effective action governing the large-scale nonlinear dynamics of such systems order by order in…
Nonlinear spin dynamics are essential in exploring nonequilibrium quantum phenomena and have broad applications in precision measurement. Among these systems, the combination of a bias magnetic field and feedback mechanisms can induce…
Two elastically coupled nanomechanical resonators driven independently near their resonance frequencies show intricate nonlinear dynamics. The dynamics provide a scheme for realizing a nanomechanical system with tunable frequency and…
This paper investigates the dynamics and integrability of the double spring pendulum, which has great importance in studying nonlinear dynamics, chaos, and bifurcations. Being a Hamiltonian system with three degrees of freedom, its analysis…
We study theoretically continuous-variable entanglement between the motional degrees of freedom of optically trapped massive particles coupled via the Coulomb interaction, in the presence of a feedback control scheme. We perform a detailed…
We consider a resonantly perturbed system of coupled nonlinear oscillators with small dissipation and outer periodic perturbation. We show that for the large time $t \sim \epsilon^{-2}$ one component of the system is described in the main…