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The paper considers a process of escape of classical particle from aone-dimensional potential well by virtue of an external harmonic forcing. Weaddress a particular model of the infinite-range potential well that allowsindependent adjustment of the well depth and of the frequency of smalloscillations. The problem can be conveniently reformulated in terms ofaction-angle variables. Further averaging provides a nontrivial conservationlaw for the slow flow. Thus, one can consider the problem in terms of averageddynamics on primary 1:1 resonance manifold. This simplification allowsefficient analytic exploration of the escape process, and yields a theoreticalprediction for minimal forcing amplitude required for the escape, as a functionof the excitation frequency. This function exhibits a single minimum forcertain intermediate frequency value. Numeric simulations are in completequalitative and reasonable quantitative agreement with the theoreticalpredictions.

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