This article is cited in 9 papers

METHODOLOGICAL NOTES

Impedance and parametric excitation of oscillators

B. Ya. Zel'dovich

CREOL College of Optics and Photonics of the University of Central Florida, Orlando, FL, USA

Abstract: This article deals with the linear ordinary differential equations for one or several coupled oscillators. Emphasis is placed on the separate notions of the frequency matrix (as a kinematic entity) and the impedance matrix. The latter matrix is explicitly introduced in this article, and its time dependence is shown to be responsible for parametric excitation and for nonconcervation of adiabatic invariants.

PACS: 05.45.Xt, 45.05.+x, 84.30.-r

Received: October 19, 2007
Revised: January 16, 2008

DOI: 10.3367/UFNr.0178.200805d.0489

 English version: Physics–Uspekhi, 2008, 51:5, 465–484

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