He's homotopy perturbation method to periodic solutions of nonlinear Jerk equations

Abstract

In this paper, He's homotopy perturbation method is applied to nonlinear Jerk equations involving the third temporal derivative of displacement. The result reveals that the first-order approximate period is identical to that obtained by the harmonic balance method. However, the high-order analytical approximate periods and periodic solutions are more accurate and in better agreement with the exact results. Thus, He's homotopy perturbation method is very effective for these third-order nonlinear differential equations.