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Zbl 1237.70036
He, Ji-Huan
Hamiltonian approach to nonlinear oscillators. (English)
[J] Phys. Lett., A 374, No. 23, 2312-2314 (2010). ISSN 0375-9601

Summary: A Hamiltonian approach to nonlinear oscillators is suggested. A conservative oscillator always admits a Hamiltonian invariant, $H$, which keeps unchanged during oscillation. This property is used to obtain approximate frequency-amplitude relationship of a nonlinear oscillator with acceptable accuracy. Two illustrating examples are given to elucidate the solution procedure.
MSC 2000:
*70H05 Hamilton's equations
70K75 Nonlinear modes
70K30 Nonlinear resonances (general mechanics)
49S05 Variational principles of physics

Keywords: nonlinear oscillator; variational principle; Hamiltonian; amplitude-frequency relationship

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