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Hamiltonian approach to nonlinear oscillators. (English) Zbl 1237.70036
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:
70H05Hamilton’s equations
70K75Nonlinear modes (general mechanics)
70K30Nonlinear resonances (general mechanics)
49S05Variational principles of physics
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