Galerkin approach to approximate solutions of some nonlinear oscillator equations

被引：9

作者：

Anderson, D. ^{[1
]}

Desaix, M. ^{[2
]}

Lisak, M. ^{[1
]}

Rasch, J. ^{[1
]}

机构：

[1] Chalmers, Dept Radio & Space Sci, SE-41296 Gothenburg, Sweden

[2] Univ Coll Boras, Sch Engn, SE-50190 Boras, Sweden

来源：

AMERICAN JOURNAL OF PHYSICS | 2010年 / 78卷 / 09期

关键词：

SIMPLE PENDULUM; PERIOD; AMPLITUDE;

D O I：

10.1119/1.3429974

中图分类号：

G40 [教育学];

学科分类号：

040101 ; 120403 ;

摘要：

An analysis based on the Galerkin method is given of some nonlinear oscillator equations that have been analyzed by several other methods, including harmonic balance and direct variational methods. The present analysis is shown to provide simple yet accurate approximate solutions of these nonlinear equations and illustrates the usefulness and the power of the Galerkin method. (C) 2010 American Association of Physics Teachers. [DOI: 10.1119/1.3429974]

引用

页码：920 / 924

页数：5

共 21 条

[1] APPROXIMATE SOLUTIONS OF SOME NON-LINEAR DIFFUSION EQUATIONS [J].

ANDERSON, D ;

LISAK, M .

PHYSICAL REVIEW A, 1980, 22 (06) :2761-2768

[2]

[Anonymous], 1981, An introduction to nonlinear oscillations

[3]

[Anonymous], 1972, The method of weighted residuals and variational principles

[4] Accurate approximate solution to nonlinear oscillators in which the restoring force is inversely proportional to the dependent variable [J].

Belendez, A. ;

Gimeno, E. ;

Fernandez, E. ;

Mendez, D. I. ;

Alvarez, M. L. .

PHYSICA SCRIPTA, 2008, 77 (06)

[5] Application of the homotopy perturbation method to the nonlinear pendulum [J].

Belendez, A. ;

Hernandez, A. ;

Belendez, T. ;

Neipp, C. ;

Marquez, A. .

EUROPEAN JOURNAL OF PHYSICS, 2007, 28 (01) :93-104

[6] Analytical approximations for the period of a nonlinear pendulum [J].

Belendez, A. ;

Hernandez, A. ;

Marquez, A. ;

Belendez, T. ;

Neipp, C. .

EUROPEAN JOURNAL OF PHYSICS, 2006, 27 (03) :539-551

[7]

Crank J., 1979, MATH DIFFUSION, V2nd

[8] SIMPLE PENDULUM APPROXIMATION [J].

GANLEY, WP .

AMERICAN JOURNAL OF PHYSICS, 1985, 53 (01) :73-76

[9] Frequencies of oscillators with fractional-power non-linearities [J].

Gottlieb, HPW .

JOURNAL OF SOUND AND VIBRATION, 2003, 261 (03) :557-566

[10]

Gradshteyn I. S., 2014, Table of Integrals, Series, andProducts

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