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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:

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