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ERIC Number: EJ901528
Record Type: Journal
Publication Date: 2010-Sep
Pages: 8
Abstractor: As Provided
Reference Count: 9
ISSN: ISSN-0143-0807
Explicit Analytical Solution of a Pendulum with Periodically Varying Length
Yang, Tianzhi; Fang, Bo; Li, Song; Huang, Wenhu
European Journal of Physics, v31 n5 p1089-1096 Sep 2010
A pendulum with periodically varying length is an interesting physical system. It has been studied by some researchers using traditional perturbation methods (for example, the averaging method). But due to the limitation of the conventional perturbation methods, the solutions are not valid for long-term prediction of the pendulum. In this paper, we use the homotopy analysis method to explore the approximate solution to this system. The method can easily self-adjust and control the convergence region. By applying the method to the governing equation of the pendulum, we obtain the approximation solution in a closed form. It is shown by the numerical method that the homotopy analysis method supplies a more accurate analytical solution for predicting the long-term behaviour of the pendulum. We believe that this system may be a good example for undergraduate and graduate students for better understanding of nonlinear oscillations. (Contains 3 figures.)
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Publication Type: Journal Articles; Reports - Descriptive
Education Level: Higher Education
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A