Liao, S. J. A second-order approximate analytical solution of a simple pendulum by the process analysis method. (English) Zbl 0769.70017 J. Appl. Mech. 59, No. 4, 970-975 (1992). Summary: A new kind of analytical method for nonlinear problems 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 by the second-order approximation are in good agreement with the numerical results. They are compared with perturbation solutions, and it appears that even the first-order solutions are more accurate than the perturbation solutions by second-order approximation. Cited in 24 Documents MSC: 70K25 Free motions for nonlinear problems in mechanics PDF BibTeX XML Cite \textit{S. J. Liao}, J. Appl. Mech. 59, No. 4, 970--975 (1992; Zbl 0769.70017) Full Text: DOI