Related papers: Capture into resonance and escape from it in a for…
We consider a classical hydrogen atom in a linearly polarized electric field of slow changing frequency. When the system passes through a resonance between the driving frequency and the Kepler frequency of the electron's motion, a capture…
Mean motion resonances are a common feature of both our own Solar System and of extrasolar planetary systems. Bodies can be trapped in resonance when their orbital semi-major axes change, for instance when they migrate through a…
Mean motion resonances are a common feature of both our own Solar System and of extrasolar planetary systems. Bodies can be trapped in resonance when their orbital semi-major axes change, for instance when they migrate through a…
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…
Forced oscillation of a system composed of two pendulums coupled by a spring in the presence of damping is investigated. In the steady state and within the small angle approximation we solve the system equations of motion and obtain the…
The process of capture of a molecular enesemble into rotational resonance in the optical centrifuge is investigated. The adiabaticity and phase space incompressibility are used to find the resonant capture probability in terms of two…
Resonance capture is studied numerically in the three-body problem for arbitrary inclinations. Massless particles are set to drift from outside the 1:5 resonance with a Jupiter-mass planet thereby encountering the web of the planet's…
We investigate a system of two weakly coupled oscillators. It is shown that an external periodic perturbation can lead to the capture into resonance. Asymptotic description and numerical simulations are presented. We have obtained the…
The humble pendulum is often invoked as the archetype of a simple, gravity driven, oscillator. Under ideal circumstances, the oscillation frequency of the pendulum is independent of its mass and swing amplitude. However, in most real-world…
A simple approximation formula is derived here for the dependence of the period of a simple pendulum on amplitude that only requires a pocket calculator and furnishes an error of less than 0.25% with respect to the exact period. It is shown…
A migrating planet can capture planetesimals into mean motion resonances. However, resonant trapping can be prevented when the drift or migration rate is sufficiently high. Using a simple Hamiltonian system for first and second order…
System of differential equations describing the initial stage of the capture of oscillatory systems into the parametric autoresonance is considered. Of special interest are solutions whose amplitude increases without bound with time. The…
The phase space for a periodically driven nonlinear oscillator consists of many resonance zones. Let the strength of periodic excitation and the strength of the damping be indexed by a small parameter $\varepsilon$. It is well known that,…
The steady state motion of a folded pendulum has been studied using frequencies of drive that are mainly below the natural (resonance) frequency of the instrument. Although the free-decay of this mechanical oscillator appears textbook…
We investigate the nonlinear effect of a pendulum with the upper end fixed to an elastic rod which is only allowed to vibrate horizontally. The pendulum will start rotating and trace a delicate stationary pattern when released without…
Based on the value of the orbital eccentricity of a particle and also its proximity to the exact resonant orbit in a three-body system, the Pendulum Approximation (Dermott & Murray 1983) or the Second Fundamental Model of Resonance (Andoyer…
We study an autoresonant asymptotic behaviour for nonlinear oscillators under slowly changing frequency and amplitude of external driver. As a result we obtain formulas for threshold values of amplitude and frequency of the driver when…
The early stages of dynamical evolution of planetary systems are often shaped by dissipative processes that drive orbital migration. In multi-planet systems, convergent amassing of orbits inevitably leads to encounters with rational period…
When the frequencies of the elastic and pendular oscillations of an elastic pendulum or swinging spring are in the ratio two-to-one, there is a regular exchange of energy between the two modes of oscillation. We refer to this phenomenon as…
The time-dependent probability density function of a system evolving towards a stationary state exhibits an oscillatory behavior if the eigenvalues of the corresponding evolution operator are complex. The frequencies \omega_n, with which…