Autoresonant (nonstationary) excitation of pendulums, Plutinos, plasmas, and other nonlinear oscillators

J. Fajans*, L. Frièdland

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

165 Scopus citations

Abstract

A weakly driven pendulum cannot be strongly excited by a fixed frequency drive. The only way to strongly excite the pendulum is to use a drive whose frequency decreases with time. Feedback is often used to control the rate at which the frequency decreases. Feedback need not be employed, however; the drive frequency can simply be swept downwards. With this method, the drive strength must exceed a threshold proportional to the sweep rate raised to the 3/4 power. This threshold has been discovered only recently, and holds for a very broad class of driven nonlinear oscillators. The threshold may explain the abundance of 3:2 resonances and dearth of 2:1 resonances observed between the orbital periods of Neptune and the Plutinos (Pluto and many of the Kuiper Belt objects), and has been extensively investigated in the Diocotron system in pure-electron plasmas.

Original languageEnglish
Pages (from-to)1096-1102
Number of pages7
JournalAmerican Journal of Physics
Volume69
Issue number10
DOIs
StatePublished - Oct 2001

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