On the analysis of internally resonant oscillators

A.M. Sommariva

doi:10.1109/31.1725

Miniaturization and Optimization of Nanoscale Resonant Oscillators

10.21236/ada595078 ◽

2013 ◽

Author(s):

Y. Fainman ◽

C. Tu ◽

V. Lomakin ◽

B. Slutsky ◽

M. Nezhad

Keyword(s):

Resonant Oscillators

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Non-Abelian quantum adiabatic dynamics and phase simulation with classical resonant oscillators

Physical Review A ◽

10.1103/physreva.102.032213 ◽

2020 ◽

Vol 102 (3) ◽

Author(s):

Y. N. Zhang ◽

J. Shen ◽

H. D. Liu ◽

X. X. Yi

Keyword(s):

Resonant Oscillators ◽

Adiabatic Dynamics

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Nonlinear Instabilities, Negative Energy Modes and Generalized Cherry Oscillators

Zeitschrift für Naturforschung A ◽

10.1515/zna-1990-0701 ◽

1990 ◽

Vol 45 (7) ◽

pp. 839-846 ◽

Cited By ~ 1

Author(s):

D. Pfirsch

Keyword(s):

Initial Conditions ◽

Complete Solution ◽

Continuum Theory ◽

Wave Interaction ◽

Negative Energy ◽

Solution Set ◽

Maxwell Theory ◽

Resonant Oscillators ◽

Simple Physical Interpretation ◽

Two Parameter

AbstractIn 1925 Cherry [1] discussed two oscillators of positive and negative energy that are nonlinearly coupled in a special way, and presented a class of exact solutions of the nonlinear equations showing explosive instability independent of the strength of the nonlinearity and the initial amplitudes. In this paper Cherry's Hamiltonian is transformed into a form which allows a simple physical interpretation. The new Hamiltonian is generalized to three nonlinearly coupled oscillators; it corresponds to three-wave interaction in a continuum theory, like the Vlasov-Maxwell theory, if there exist linear negative energy waves [2-4, 5, 6], Cherry was able to present a two-parameter solution set for his example which would, however, allow a four-parameter solution set, and, as a first result, an analogous three-parameter solution set for the resonant three-oscillator case is obtained here which, however, would allow a six-parameter solution set. Nonlinear instability is therefore proven so far only for a very small part of the phase space of the oscillators. This paper gives in addition the complete solution for the three-oscillator case and shows that, except for a singular case, all initial conditions, especially those with arbitrarily small amplitudes, lead to explosive behaviour. This is true of the resonant case. The non-resonant oscillators can sometimes also become explosively unstable, but the initial amplitudes must not be infinitesimally small. A few examples are presented for illustration.

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