Related papers: On forced oscillations in groups of interacting no…
Summary: A system of autonomous ordinary differential equations depending on a small parameter is considered such that the unperturbed system has an invariant manifold of periodic solutions that is not normally hyperbolic but is normally…
When a dynamical system contains several different modes of oscillations it may behave in a variety of ways: If the modes oscillate at their own individual frequencies, it exhibits quasiperiodic behavior; when the modes lock to one another…
We present an adequate analytical approach to the description of nonlinear vibration with strong energy exchange between weakly coupled oscillators and oscillatory chains. The fundamental notion of the limiting phase trajectory (LPT)…
The gravitational-radiation-induced inspiral of a binary system of compact objects is considered. A scheme is described to model the regime in which the gravitational interaction is too strong to use weak-field approximation methods, but…
It is rigorously proved that quasilinear impulsive systems possess unpredictable solutions when a perturbation generated by an unpredictable sequence is applied. The existence, uniqueness, as well as asymptotic stability of such solutions…
Normally, in mathematics and physics, only point particle systems, which are either finite or countable, are studied. We introduce new formal mathematical object called regular continuum system of point particles (with continuum number of…
We analyse a one-dimensional model of hard particles, within ensembles of trajectories that are conditioned (or biased) to atypical values of the time-averaged dynamical activity. We analyse two phenomena that are associated with these…
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…
We provide sufficient conditions for the existence of periodic solutions with small amplitude of the non--linear planar double pendulum perturbed by smooth or non--smooth functions.
Mechanisms are elucidated underlying the existence of dynamical systems whose generic solutions approach asymptotically (at large time) isochronous evolutions: all their dependent variables tend asymptotically to functions periodic with the…
This paper considers systems subject to nonholonomic constraints which are not uniform on the whole configuration manifold. When the constraints change, the system undergoes a transition in order to comply with the new imposed conditions.…
A chaotic system under periodic forcing can develop a periodically visited strange attractor. We discuss simple models in which the phenomenon, quite easy to see in numerical simulations, can be completely studied analytically.
We perform a detailed study of the dynamics of a nonlinear, one-dimensional oscillator driven by a periodic force under hysteretic damping, whose linear version was originally proposed and analyzed by Bishop in [1]. We first add a small…
A geometric form of Euler-Lagrange equations is developed for a chain pendulum, a serial connection of $n$ rigid links connected by spherical joints, that is attached to a rigid cart. The cart can translate in a horizontal plane acted on by…
Collective actuation in active solids - the spontaneous coherent excitation of a few vibrational modes - emerges from a feedback between structural deformations and the orientation of active forces. It is an excellent candidate as a basic…
Oscillations in a power system can be categorized into free oscillations and forced oscillations. Many algorithms have been developed to estimate the modes of free oscillations in a power system. Recently, forced oscillations caught many…
In this letter, we experimentally demonstrate an efficient scheme to regulate the behaviour of coupled nonlinear oscillators through dynamic control of their interaction. It is observed that introducing intermittency in the interaction term…
The motion of a thin elastic plate interacting with a viscous fluid is investigated. A periodic force acting on the plate is considered, which in a setting without damping could lead to a resonant response. The interaction with the viscous…
A classical double oscillator model, that includes in certain parameter limits, the standard harmonic oscillator and the inverse oscillator, is interpreted as a dynamical system. We study its essential features and make a qualitative…
We investigate a torsional pendulum containing a ferrofluid that is forced periodically to undergo small-amplitude oscillations. A homogeneous magnetic field is applied perpendicular to the pendulum axis. We give an analytical formula for…