Improvement of Harmonic Balance Using Jacobian Elliptic Functions

作     者：Serge Bruno Yamgoué Bonaventure Nana Olivier Tiokeng Lekeufack 

作者机构：Department of Physics Higher Teacher Training College-Bambili The University of Bamenda Bamenda Cameroon Laboratory of Mechanics Department of Physics Faculty of Science The University of Yaoundé 1 Yaoundé Cameroon 

出 版 物：《Journal of Applied Mathematics and Physics》 (应用数学与应用物理（英文）)

年 卷 期：2015年第3卷第6期

页      面：680-690页

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：Harmonic Balance Linearization Continuous Force Function Single Degree-of-Freedom Conservative System Jacobian Elliptic Functions Symmetric Oscillations 

摘      要：We propose a method for finding approximate analytic solutions to autonomous single degree-of-freedom nonlinear oscillator equations. It consists of the harmonic balance with linearization in which Jacobian elliptic functions are used instead of circular trigonometric functions. We show that a simple change of independent variable followed by a careful choice of the form of anharmonic solution enable to obtain highly accurate approximate solutions. In particular our examples show that the proposed method is as easy to use as existing harmonic balance based methods and yet provides substantially greater accuracy.