NotesFAQContact Us
Search Tips
Peer reviewed Peer reviewed
Direct linkDirect link
ERIC Number: EJ827975
Record Type: Journal
Publication Date: 2007-Jan
Pages: 12
Abstractor: As Provided
Reference Count: 21
ISSN: ISSN-0143-0807
Application of the Homotopy Perturbation Method to the Nonlinear Pendulum
Belendez, A.; Hernandez, A.; Belendez, T.; Marquez, A.
European Journal of Physics, v28 n1 p93-104 Jan 2007
The homotopy perturbation method is used to solve the nonlinear differential equation that governs the nonlinear oscillations of a simple pendulum, and an approximate expression for its period is obtained. Only one iteration leads to high accuracy of the solutions and the relative error for the approximate period is less than 2% for amplitudes as high as 130 degrees. Another important point is that this method provides an analytical expression for the angular displacement as a function of time as the sum of an infinite number of harmonics; although for practical purposes it is sufficient to consider only a finite number of harmonics. We believe that the present study may be a suitable and fruitful exercise for teaching and better understanding perturbation techniques in advanced undergraduate courses on classical mechanics. (Contains 1 figure.)
Institute of Physics Publishing. The Public Ledger Building Suite 929, 150 South Independence Mall West, Philadelphia, PA 19106. Tel: 215-627-0880; Fax: 215-627-0879; e-mail:; Web site:
Publication Type: Journal Articles; Reports - Research
Education Level: N/A
Audience: Teachers
Language: English
Sponsor: N/A
Authoring Institution: N/A