Analytical analysis for large-amplitude oscillation of a rotational pendulum system

Siu Kai Lai; C. W. Lim; Zhang Lin; W. Zhang

doi:10.1016/j.amc.2010.12.089

Analytical analysis for large-amplitude oscillation of a rotational pendulum system

Siu Kai Lai
, C. W. Lim
, Zhang Lin
, W. Zhang

Research output: Journal article publication › Journal article › Academic research › peer-review

24 Citations (Scopus)

Abstract

This paper deals with large amplitude oscillation of a nonlinear pendulum attached to a rotating structure. By coupling of the well-known Maclaurin series expansion and orthogonal Chebyshev polynomials, the governing differential equation with sinusoidal nonlinearity can be reduced to form a cubic-quintic Duffing equation. The resulting Duffing type temporal problem is solved by an analytic iteration approach. Two approximate formulas for the frequency (period) and the periodic solution are established for small as well as large amplitudes of motion. Illustrative examples are selected and compared to those analytical and exact solutions to substantiate the accuracy and correctness of the approximate analytical approach.

Original language	English
Pages (from-to)	6115-6124
Number of pages	10
Journal	Applied Mathematics and Computation
Volume	217
Issue number	13
DOIs	https://doi.org/10.1016/j.amc.2010.12.089
Publication status	Published - 1 Mar 2011
Externally published	Yes

Keywords

Chebyshevs polynomials
Cubic-quintic Duffing equation
Maclaurin series
Rotational pendulum system

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

More information

10.1016/j.amc.2010.12.089

Cite this

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title = "Analytical analysis for large-amplitude oscillation of a rotational pendulum system",

abstract = "This paper deals with large amplitude oscillation of a nonlinear pendulum attached to a rotating structure. By coupling of the well-known Maclaurin series expansion and orthogonal Chebyshev polynomials, the governing differential equation with sinusoidal nonlinearity can be reduced to form a cubic-quintic Duffing equation. The resulting Duffing type temporal problem is solved by an analytic iteration approach. Two approximate formulas for the frequency (period) and the periodic solution are established for small as well as large amplitudes of motion. Illustrative examples are selected and compared to those analytical and exact solutions to substantiate the accuracy and correctness of the approximate analytical approach.",

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AU - Lai, Siu Kai

AU - Lim, C. W.

AU - Lin, Zhang

AU - Zhang, W.

PY - 2011/3/1

Y1 - 2011/3/1

N2 - This paper deals with large amplitude oscillation of a nonlinear pendulum attached to a rotating structure. By coupling of the well-known Maclaurin series expansion and orthogonal Chebyshev polynomials, the governing differential equation with sinusoidal nonlinearity can be reduced to form a cubic-quintic Duffing equation. The resulting Duffing type temporal problem is solved by an analytic iteration approach. Two approximate formulas for the frequency (period) and the periodic solution are established for small as well as large amplitudes of motion. Illustrative examples are selected and compared to those analytical and exact solutions to substantiate the accuracy and correctness of the approximate analytical approach.

AB - This paper deals with large amplitude oscillation of a nonlinear pendulum attached to a rotating structure. By coupling of the well-known Maclaurin series expansion and orthogonal Chebyshev polynomials, the governing differential equation with sinusoidal nonlinearity can be reduced to form a cubic-quintic Duffing equation. The resulting Duffing type temporal problem is solved by an analytic iteration approach. Two approximate formulas for the frequency (period) and the periodic solution are established for small as well as large amplitudes of motion. Illustrative examples are selected and compared to those analytical and exact solutions to substantiate the accuracy and correctness of the approximate analytical approach.

KW - Chebyshevs polynomials

KW - Cubic-quintic Duffing equation

KW - Maclaurin series

KW - Rotational pendulum system

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DO - 10.1016/j.amc.2010.12.089

M3 - Journal article

SN - 0096-3003

VL - 217

SP - 6115

EP - 6124

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

IS - 13

ER -

Analytical analysis for large-amplitude oscillation of a rotational pendulum system

Abstract

Keywords

ASJC Scopus subject areas

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