An Approximate Solution for a Simple Pendulum beyond the Small Angles Regimes Using Hybrid Artificial Neural Network and Particle Swarm Optimization Algorithm

摘要

Simple pendulum is the most popular example in mechanics. Study on the physics of simple pendulum is a key to understanding the nonlinear dynamics of many other systems. However, there is an exact analytical solution for this problem, but its exact solution is in the form of the Jacobi elliptic integral which it is hard for using in simple engineering manipulations. Hence, determining an accurate simple approximate solution is helpful. This study presents a new method by using hybrid neural networks and particle swarm optimization algorithm, in order to find a simple approximate solution for motion of a nonlinear pendulum beyond the small angles regime. The approximate solution is simple and powerful to converge to the exact solution. The results of the approximate solution are compared with exact solution and linear solution, using tables and graphs. Furthermore, the present method is expandable to solve complex pendulums.