A unified Krylov-Bogoliubov-Mitropolskii method for solving nth order nonlinear systems

被引：33

作者：

Alam, MS ^{[1
]}

机构：

[1] Bangladesh Inst Technol, Dept Math, Rajshahi 6204, Bangladesh

来源：

JOURNAL OF THE FRANKLIN INSTITUTE-ENGINEERING AND APPLIED MATHEMATICS | 2002年 / 339卷 / 02期

关键词：

Control nonlinearities - Damping - Linear equations - Ordinary differential equations - Oscillations;

D O I：

10.1016/S0016-0032(02)00020-0

中图分类号：

TP [自动化技术、计算机技术];

学科分类号：

0812 ;

摘要：

A unified theory is presented for obtaining the transient response of nth order nonlinear systems with small nonlinearities by Krylov-Bogoliubov-Mitropolskii method. The method is a generalization of Bogoliubov's asymptotic method and covers all three cases when the roots of the corresponding linear equation are real, complex conjugate, or purely imaginary. It is shown that by suitable substitution for the roots in the general result that the solution corresponding to each of the three cases can be obtained. The method is illustrated by examples. (C) 2002 Published by Elsevier Science Ltd. on behalf of The Franklin Institute.

引用

页码：239 / 248

页数：10

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