Abstract
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.
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Original Russian Text © Yu.V. Brezhnev, S.V. Sazonov, 2014, published in Zhurnal Eksperimental’noi i Teoreticheskoi Fiziki, 2014, Vol. 146, No. 5, pp. 1106–1121.
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Brezhnev, Y.V., Sazonov, S.V. On the nonlinear dissipative dynamics of weakly overdamped oscillators. J. Exp. Theor. Phys. 119, 971–984 (2014). https://doi.org/10.1134/S1063776114110028
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DOI: https://doi.org/10.1134/S1063776114110028