English

Escape of harmonically forced classical particle from an infinite-range potential well

Classical Physics 2017-09-28 v2 Dynamical Systems Chaotic Dynamics

Abstract

The paper considers a process of escape of classical particle from a one-dimensional potential well by virtue of an external harmonic forcing. We address a particular model of the infinite-range potential well that allows independent adjustment of the well depth and of the frequency of small oscillations. The problem can be conveniently reformulated in terms of action-angle variables. Further averaging provides a nontrivial conservation law for the slow flow. Thus, one can consider the problem in terms of averaged dynamics on primary 1:1 resonance manifold. This simplification allows efficient analytic exploration of the escape process, and yields a theoretical prediction for minimal forcing amplitude required for the escape, as a function of the excitation frequency. This function exhibits a single minimum for certain intermediate frequency value. Numeric simulations are in complete qualitative and reasonable quantitative agreement with the theoretical predictions.

Keywords

Cite

@article{arxiv.1704.06924,
  title  = {Escape of harmonically forced classical particle from an infinite-range potential well},
  author = {O. V. Gendelman},
  journal= {arXiv preprint arXiv:1704.06924},
  year   = {2017}
}