期刊目錄列表 - 11~20期(1966-1975) - 第二十期 (1975)
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以傑畢雪夫多項式處理非線性平面擺近似週期的計算
作者:許榮富

摘要:

諧振問題於討論工程學、物理學,尤其電路上等之動力性質時,占著最基礎且極重要之地位。理論處理上因加疊原理在非線性微分方程中不能應用,即欲求一非線性系對二個不同力函數之反應時,此二力函數合成所求得之結果,將不同於此二力各別效應之和,也即基本上每一非線性諧振問題即成為一個特例,傳統幾法中,具有代表性的是:微擾方法(Perturbation Method),逐次近似法(Successive Approximation Method),循環函數解法(Periodic Solution Method),降階分離變數法(Kryloff and Bogoliuboff's Method)等等,每一方法都有其獨特之優點及缺點。此地特別介紹以另一不同的方法處理同一問題,所採用的方法是,把非線性平面擺的二階微分方程,使用傑畢雪夫多項式將其法化成線性的二階微分方程,以求得其週期,我們發現使用此方法是相當地快捷精確,且易於應用。為證實其準確,特使用計算機比較使用此方法與傳統方法之結果。最後於附錄B中再舉非線性的L.R.C.問題為實例,證實此方法是很值得推薦的。

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Journal directory listing - Volume 11-20 (1966-1975) - Volume 20 (1975)
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Chebyshev Polynomials in Non-Linear Plane Pendulum Problem
Author: Joung-Fu Hsu

Abstract:

The treatment of oscillation problems by linear equations is only a first approximation. There are nonlinear terms in the equation of horizontal motion of a plane pendulum. The effect of these nonlinearities has been reviewed by a traditional method such as Perturbation Method. The purpose of the paper are to enhance the another mathematical method of improving the accuracy obtainable by linearization of the Chebyshev Polynomials and strongly to recommend the extendible appli cation of Chebyshev Polynomials to the non-linear oscillation problems.