Approximate first integrals of weakly nonlinear, damped-driven oscillators with one degree of freedom

被引：7
|
作者：
Ünal, G [1 ]
机构：
[1] Istanbul Tech Univ, Fac Sci & Letters, TR-80626 Istanbul, Turkey
来源：
NONLINEAR DYNAMICS | 2001年 / 26卷 / 04期
关键词：
approximate symmetries; resonances; approximate first integrals; bifurcations;
D O I：
10.1023/A:1013331523696
中图分类号：
TH [机械、仪表工业];
学科分类号：
0802 ;
摘要：
First-order approximate symmetries of weakly nonlinear, damped-driven oscillators have been determined. First-order approximate first integrals have been obtained by employing an approximate version of Noether's theorem for the conservative case. Furthermore, approximate first integrals of the damped case have been obtained based on the first integrals of the conservative case. Approximate first integrals enabled us to identify three types of generic bifurcations. Analytical results have been verified by numerical experiments.
引用
收藏
页码：309 / 329
页数：21
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