Effective Hamiltonians for resonance interaction dynamics and interdisciplinary analogies

摘要

Resonance interactions of oscillators are responsible for fundamental effects in different areas of physics and classical mechanics. The resonance between any two oscillators/modes destroys their individuality by generating a new effective oscillator of energy flow between the two parent oscillators, which is known as beating. In particular, the fundamental character of such energy exchange oscillators is revealed by the fact of their exact integrability in many physically reasonable cases. The present work illustrates such a standpoint on elastic oscillators, discrete liquid sloshing models, and 'macroscopic' quantum dynamics related to Josephson's effects. In the case of elastic oscillations, a strongly nonlinear conservative oscillator describing the dynamics of energy partition between two identical linearly coupled oscillators with polynomial restoring force characteristics is analyzed.