The inverted pendulum: A singularity theory approach

被引：25

作者：

Broer, HW ^{[1
]}

Hoveijn, I ^{[1
]}

van Noort, M ^{[1
]}

Vegter, G ^{[1
]}

机构：

[1] Univ Groningen, Dept Math, NL-9700 AV Groningen, Netherlands

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 1999年 / 157卷 / 01期

关键词：

D O I：

10.1006/jdeq.1998.3623

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The inverted pendulum with small parametric forcing is considered as an example of a wider class of parametrically forced Hamiltonian systems. The qualitative dynamics of the Poincare map corresponding to the central periodic solution is studied via an approximating integrable normal form. At bifurcation points we construct local universal models in the appropriate symmetry context, using equivariant singularity theory. In this context, structural stability can be proved under generic conditions. (C) 1999 Academic Press.

引用

页码：120 / 149

页数：30

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