A Second-Order Approximate Analytical Solution of a Simple Pendulum by the Process Analysis Method

[+] Author and Article Information
S. J. Liao

Institute of Shipbuilding, University of Hamburg, Laemmerseith 90, D-2000 Hamburg 60, Federal Republic of Germany

J. Appl. Mech 59(4), 970-975 (Dec 01, 1992) (6 pages) doi:10.1115/1.2894068 History: Received May 05, 1990; Revised September 30, 1991; Online March 31, 2008


In this paper, a new kind of analytical method of nonlinear problem called the process analysis method (PAM) is described and used to give a second-order approximate solution of a simple pendulum. The PAM does not depend on the small parameter supposition and therefore can overcome the disadvantages and limitations of the perturbation expansion method. The analytical approximate results at the second-order of approximation are in good agreement with the numerical results. They are compared with perturbation solutions, and it appears that even the firstorder solutions are more accurate than the perturbation solutions at second-order of approximation.

Copyright © 1992 by The American Society of Mechanical Engineers
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