|
This article is cited in 3 scientific papers (total in 3 papers)
Nonstationary Energy Localization vs Conventional Stationary Localization in Weakly Coupled Nonlinear Oscillators
Leonid I. Manevitcha, Agnessa Kovalevab, Grigori Sigalovc a Institute of Chemical Physics, Russian Academy of Sciences, ul. Kosygina 4, Moscow, 119991, Russia
b Space Research Institute, Russian Academy of Sciences, ul. Profsoyuznaya 84/32, Moscow, 117997, Russia
c University of Illinois at Urbana-Champaign, Urbana, IL, 61801, USA
Abstract:
In this paper we study the effect of nonstationary energy localization in a nonlinear conservative resonant system of two weakly coupled oscillators. This effect is alternative to the well-known stationary energy localization associated with the existence of localized normal modes and resulting from a local topological transformation of the phase portraits of the system. In this work we show that nonstationary energy localization results from a global transformation of the phase portrait. A key to solving the problem is the introduction of the concept of limiting phase trajectories (LPTs) corresponding to maximum possible energy exchange between the oscillators. We present two scenarios of nonstationary energy localization under the condition of 1:1 resonance. It is demonstrated that the conditions of nonstationary localization determine the conditions of efficient targeted energy transfer in a generating dynamical system. A possible extension to multi-particle systems is briefly discussed.
Keywords:
nonlinear oscillations, coupled oscillators, nonlinear resonances, systems with slow and fast motions.
Received: 11.04.2015 Accepted: 10.10.2015
Citation:
Leonid I. Manevitch, Agnessa Kovaleva, Grigori Sigalov, “Nonstationary Energy Localization vs Conventional Stationary Localization in Weakly Coupled Nonlinear Oscillators”, Regul. Chaotic Dyn., 21:2 (2016), 147–159
Linking options:
https://www.mathnet.ru/eng/rcd71 https://www.mathnet.ru/eng/rcd/v21/i2/p147
|
Statistics & downloads: |
Abstract page: | 202 | References: | 47 |
|