Impedance and parametric excitation of oscillators

B.Ya. Zel’dovich^a, b
^aUniversity Academic Division of Nonlinear Optics, Institute of Electro-Physics of the Ural Division of the Russian Academy of Sciences, pr. Lenina 76, Chelyabinsk, 454010, Russian Federation
^bCollege of Optics and Photonics/CREOL, University of Central Florida, 4000 Central Florida Blvd., Orlando, Florida, 32816-2700, USA

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 nonconservation of adiabatic invariants.

PACS: 05.45.Xt, 45.05.+x, 84.30.−r (all)
DOI: 10.1070/PU2008v051n05ABEH006498
URL: https://ufn.ru/en/articles/2008/5/d/
Web of Science

000259376200004
Scopus

2-s2.0-51549117543
ADS NASA

2008PhyU...51..465Z
Citation: Zel’dovich B Ya "Impedance and parametric excitation of oscillators" Phys. Usp. 51 465–484 (2008)

BibTexBibNote ® (generic)BibNote ® (RIS)MedlineRefWorks

Оригинал: Зельдович Б Я «Импеданс и параметрическое возбуждение осцилляторов» УФН 178 489–510 (2008); DOI: 10.3367/UFNr.0178.200805d.0489