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 publicationJournal articleAcademic researchpeer-review

17 Citations (Scopus)


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 languageEnglish
Pages (from-to)6115-6124
Number of pages10
JournalApplied Mathematics and Computation
Issue number13
Publication statusPublished - 1 Mar 2011
Externally publishedYes


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

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics


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