Related papers: Capture into resonance and escape from it in a for…
Autoresonance is a phase locking phenomenon occurring in nonlinear oscillatory system, which is forced by oscillating perturbation. Many physical applications of the autoresonance are known in nonlinear physics. The essence of the…
A restricted planar circular three-body system, consisting of the Sun and two planets, is studied as a simple model for a planetary system. The mass of the inner planet is considered to be larger and the system is assumed to be moving in a…
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…
Planets undergoing convergent migration can be captured into mean-motion resonance (MMR), in which the planets' periods are related by integer ratios. The dynamics of MMR are typically considered in isolation, including only the forces…
A mathematical model describing the initial stage of the capture of oscillatory systems into autoresonance under the action of slowly varying pumping is considered. Solutions with an infinitely growing amplitude are associated with the…
We study numerically a discrete, nonlinear lattice, which is formed by a chain of pendula submitted to a harmonic-driving source with constant amplitude and parametrical excitation. A supratransmission phenomenon is obtained after the…
Consider a periodically forced nonlinear system which can be presented as a collection of smaller subsystems with pairwise interactions between them. Each subsystem is assumed to be a massive point moving with friction on a compact surface,…
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…
When two systems are coupled, the driver system can function as an external forcing over the driven or response system. Also, an external forcing can independently perturb the driven system, leading us to examine the interplay between the…
Since Galileo's time, the pendulum has evolved into one of the most exciting physical objects in mathematical modeling due to its vast range of applications for studying various oscillatory dynamics, including bifurcations and chaos, under…
Structural resonance involves the absorption of inertial loads by a tuned structural elasticity: a process playing a key role in a wide range of biological and technological systems, including many biological and bio-inspired locomotion…
Non-autonomous perturbations of isochronous systems in the plane are considered. It is assumed that the intensity of perturbations decays with time, and the frequency is asymptotically constant with the limiting value satisfying a resonance…
The resonant activation phenomenon (RAP) in a discrete system is studied using the master equation formalism. We show that the RAP corresponds to a non-monotonic behavior of the frequency dependent first passage time probability density…
Migration of planetary systems caused by the action of dissipative forces may lead the planets to be trapped in a resonance. In this work we study the conditions and the dynamics of such resonant trapping. Particularly, we are interested in…
We analyze the dynamics of a driven, damped pendulum as used in mechanical clocks. We derive equations for the amplitude and phase of the oscillation, on time scales longer than the pendulum period. The equations are first order ODEs and…
Strong frequency dependence is unlikely in diffusive or over-damped systems. When exceptions do occur, such as in the case of stochastic resonance, it signals an interesting underlying phenomenon. We find that such a case appears in the…
We consider a class of parametrically forced Hamiltonian systems with one-and-a-half degrees of freedom and study the stability of the dynamics when the frequency of the forcing is relatively high or low. We show that, provided the…
Following the general numerical analysis of Melita and Woolfson (1996), I showed in a recent paper that a restricted, planar, circular planetary system consisting of Sun, Jupiter and Saturn would be captured in a near (2:1) resonance when…
The motion of a simple pendulum in a uniform gravitational field can be described by the solution of a second-order differential equation, nonlinear differential equation. In practice we solve this equation using the small angle…
A method is presented for tracing the locus of a specific peak in the frequency response under variation of a parameter. It is applicable to periodic, steady-state vibrations of harmonically forced nonlinear mechanical systems. It operates…