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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 (should also be assigned at least one other classification number in Section 49-XX)
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