An Approximate Analytical Approach to Investigate the Stability and Response of Holonomic Problems in Classic Dynamics by Means of the Homotopy Perturbation Method

Department of Mechanical and Manufacturing Engineering, Aalborg University, Pontoppidanstraede 101, DK-9220 Aalborg East, Denmark

In this work, a powerful analytical method called homotopy perturbation method (HPM) is used to obtain the series solution for nonlinear problems in classic dynamics. The governing equations are obtained using the Lagrange method and solved analytically by HPM. The present solution gives an expression which is valid for the whole domain of the solution. Comparisons of the obtained solutions with numerical results indicate that HPM is effective and convenient for solving holonomic problems and can be used in the same way for other nonlinear problems.