“Resonance Overlap”的概念、定义、习题解题方法及翻译-数学辞典

单词

Resonance Overlap

释义

Resonance Overlap

Isolated resonances in a Dynamical System can cause considerable distortion of preserved Tori in theirNeighborhood, but they do not introduce any Chaos into a system. However, when two or more resonances aresimultaneously present, they will render a system nonintegrable. Furthermore, if they are sufficiently ``close'' to eachother, they will result in the appearance of widespread (large-scale) Chaos.

To investigate this problem, Walker and Ford (1969) took the integrable Hamiltonian

and investigated the effect of adding a 2:2 resonance and a 3:2 resonance

At low energies, the resonant zones are well-separated. As the energy increases, the zones overlap and a ``macroscopic zoneof instability'' appears. When the overlap starts, many higher-order resonances are also involved so fairly large areas ofPhase Space have their Tori destroyed and the ensuing Chaos is ``widespread'' sincetrajectories are now free to wander between regions that previously were separated by nonresonant Tori.

Walker and Ford (1969) were able to numerically predict the energy at which the overlap of the resonances first occurred. They plotted the -axis intercepts of the inner 2:2 and the outer 2:3 separatrices as a function of total energy. The energy at which they crossed was found to be identical to that at which 2:2 and 2:3 resonance zones began to overlap.

See also Chaos, Resonance Overlap Method

References

Walker, G. H. and Ford, J. ``Amplitude Instability and Ergodic Behavior for Conservative Nonlinear Oscillator Systems.'' Phys. Rev. 188, 416-432, 1969.

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