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Title: On the nonlinear dissipative dynamics of weakly overdamped oscillators

We consider the motion of weakly overdamped linear oscillators. Weak overdamping of an oscillator is defined as a slight excess of the damping decrement over its natural frequency. Exact solutions are obtained for a certain relation between the decrement and the natural frequency and qualitatively different regimes of motion are analyzed. The threshold conditions corresponding to changes of regimes are established; one-component models with an arbitrary degree of nonlinearity are analyzed, and quadratic and cubic nonlinearities are considered in detail. If the nonlinearity in a multicomponent model is determined by a homogeneous function, transformations of the Kummer-Liouville type can be reduced to an autonomous system of second-order differential equations in the case when the relation between the decrement and the natural frequency has been established. Some integrable multicomponent models with quadratic and cubic nonlinearities are analyzed.
Authors:
 [1] ;  [2]
  1. Tomsk State University (Russian Federation)
  2. National Research Center “Kurchatov Institute” (Russian Federation)
Publication Date:
OSTI Identifier:
22309094
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Experimental and Theoretical Physics; Journal Volume: 119; Journal Issue: 5; Other Information: Copyright (c) 2014 Pleiades Publishing, Inc.; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; DAMPING; DIFFERENTIAL EQUATIONS; EXACT SOLUTIONS; INTEGRAL CALCULUS; MATHEMATICAL MODELS; NONLINEAR PROBLEMS; OSCILLATORS