Table of Contents
Journal of Nonlinear Dynamics
Volume 2013 (2013), Article ID 824701, 9 pages
http://dx.doi.org/10.1155/2013/824701
Research Article

Stabilization of Driven Pendulum with Periodic Linear Forces

COMSATS Institute of Information Technology, Islamabad 44000, Pakistan

Received 27 March 2013; Revised 18 August 2013; Accepted 23 August 2013

Academic Editor: Huai-Ning Wu

Copyright © 2013 Babar Ahmad. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Using Kapitza method of averaging for arbitrary periodic forces, the pendulum driven by different forms of periodic piecewise linear forces is stabilized. These periodic piecewise linear forces are selected in the range to establish an exact comparison with harmonic forces. In this contest, the rectangular force was found to be the best, but this force is more effective when it has a time-dependent structure. This time-dependent structure is found by defining a parametric control on some other periodic piecewise linear forces.