A reversible bifurcation analysis of the inverted pendulum

被引：22

作者：

Broer, HW ^{[1
]}

Hoveijn, I ^{[1
]}

van Noort, M ^{[1
]}

机构：

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

来源：

PHYSICA D | 1998年 / 112卷 / 1-2期

关键词：

parametrically forced oscillator; spatio-temporal symmetry; Hamiltonian system; normal form theory; equivariant singularity theory;

D O I：

10.1016/S0167-2789(97)00201-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

The inverted pendulum with a periodic parametric forcing is considered as a bifurcation problem in the reversible setting. Parameters are given by the size of the forcing and the frequency ratio. Normal form theory provides an integrable approximation of the Poincare map generated by a planar vector field. Genericity of the model is studied by a perturbation analysis, where the spatial symmetry is optional. Here equivariant singularity theory is used.

引用

页码：50 / 63

页数：14

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