TY - JOUR
T1 - Autoresonant (nonstationary) excitation of pendulums, Plutinos, plasmas, and other nonlinear oscillators
AU - Fajans, J.
AU - Frièdland, L.
PY - 2001/10
Y1 - 2001/10
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=0040485276&partnerID=8YFLogxK
U2 - 10.1119/1.1389278
DO - 10.1119/1.1389278
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AN - SCOPUS:0040485276
SN - 0002-9505
VL - 69
SP - 1096
EP - 1102
JO - American Journal of Physics
JF - American Journal of Physics
IS - 10
ER -