Extension and Application of Newton’s Method in Nonlinear Oscillation Theory

Huo Lin-chun

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 1992 > 13(9): 829-842

Huo Lin-chun. Extension and Application of Newton’s Method in Nonlinear Oscillation Theory[J]. Applied Mathematics and Mechanics, 1992, 13(9): 829-842.

Citation:

Huo Lin-chun. Extension and Application of Newton’s Method in Nonlinear Oscillation Theory[J]. Applied Mathematics and Mechanics, 1992, 13(9): 829-842.

Citation:

Huo Lin-chun. Extension and Application of Newton’s Method in Nonlinear Oscillation Theory[J]. Applied Mathematics and Mechanics, 1992, 13(9): 829-842.

PDF( 784 KB)

Extension and Application of Newton’s Method in Nonlinear Oscillation Theory

Huo Lin-chun

Tianjin University, Tianjin

Received Date: 1990-01-05
Publish Date: 1992-09-15

Abstract

Abstract

In this paper we suggest and prove that Newton's method may calculate the asymptotic analytic periodic solution of strong and weak nonlinear nonautonomous systems, so that a new analytic method is offered for studying strong and weak nonlinear oscillation systems. On the strength of the need of our method, we discuss the existence and calculation of the periodic solution of the second order nonhomogeneous linear periodic system. Besides, we investigate the application of Newton's method to quasi-linear systems. The periodic solution of Duffing equation is calculated by means of our method.
- Newton’s method,
- resonance,
- nonresonance,
- strongly nonlinear systems,
- truncated equations

FullText(HTML)

References(11)

References

[1]	李正元、钱敏,向量场的旋转度理论及其应用,北京大学出版社,北京(1982).
[2]	Боголюбов Н.Н.ц Ю.А.Митролъский,Асцмпмомцческце Мемобы Нелцнейных Колебанцй ИЗД 4-е,М,Наука(1974).
[3]	马尔金,И,Г.《非线性振动理论中的李雅普诺夫与邦加来方法》,科学出版社,北京(1959).
[4]	Nayfeh and Mook,Nonlinear Oscillations,New york(1979).
[5]	徐兆,非线性力学中的一种新的渐近方法,力学学报,17(3)(1985).
[6]	Li Li(李骊),The periodic solution of quasiconservative system,Proceedings of the Int,conf,on Nonl.,Mech,Science Press(1985).
[7]	Burton,T.D.,Nonlinear oscillation limit cycle analysis using a time transfor-mation approach,Int.J,Nonlinear Mech.,17(1)(]982).
[8]	Канторович Л.В.и Т.П,Акилов《泛函分析》,高等教育出版社,北京(1984).
[9]	欧阳光中,《数学分析》,高等教育出版社(1985).
[10]	Канторович Л.В.и В.И.Соболев.Эпеменмы Функццоналъносо аналцза,Издатслъство Наука,Москва(1965).
[11]	林千博,《物理系统中的非线性振动》,东北工学院理论力学教研室译(1980).