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

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Original languageEnglish
Pages (from-to)6115-6124
Journal / PublicationApplied Mathematics and Computation
Issue number13
Publication statusPublished - 1 Mar 2011


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. © 2010 Elsevier Inc. All rights reserved.

Research Area(s)

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