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He, Ji-Huan

Hamiltonian approach to nonlinear oscillators. (English) Zbl 1237.70036

Phys. Lett., A 374, No. 23, 2312-2314 (2010).
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.

Cited in 42 Documents

MSC:

70H05 Hamilton’s equations
70K75 Nonlinear modes
70K30 Nonlinear resonances for nonlinear problems in mechanics
49S05 Variational principles of physics

Keywords:

nonlinear oscillator; variational principle; Hamiltonian; amplitude-frequency relationship
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\textit{J.-H. He}, Phys. Lett., A 374, No. 23, 2312--2314 (2010; Zbl 1237.70036)
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References:

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