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Accurate analytical solutions to nonlinear oscillators by means of the Hamiltonian approach

✍ Scribed by M. Akbarzade; A. Kargar

Publisher
John Wiley and Sons
Year
2011
Tongue
English
Weight
275 KB
Volume
34
Category
Article
ISSN
0170-4214

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✦ Synopsis

The purpose of this paper is to apply the Hamiltonian approach to nonlinear oscillators. The Hamiltonian approach is applied to derive highly accurate analytical expressions for periodic solutions or for approximate formulas of frequency. A conservative oscillator always admits a Hamiltonian invariant, H, which stays unchanged during oscillation. This property is used to obtain approximate frequency-amplitude relationship of a nonlinear oscillator with high accuracy. A trial solution is selected with unknown parameters. Next, the Ritz-He method is used to obtain the unknown parameters. This will yield the approximate analytical solution of the nonlinear ordinary differential equations.

In contrast with the traditional methods, the proposed method does not require any small parameter in the equation.

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