A REVERSIBLE BIFURCATION-ANALYSIS OF THE INVERTED PENDULUM

Authors
BROER HW HOVEIJN I VANNOORT M
Citation
Hw. Broer et al., A REVERSIBLE BIFURCATION-ANALYSIS OF THE INVERTED PENDULUM, Physica. D, 112(1-2), 1998, pp. 50-63
Citations number
29
Categorie Soggetti
Physycs, Mathematical",Physics,"Physycs, Mathematical
Journal title
Physica. D → ACNP
ISSN journal
01672789
Volume
112
Issue
1-2
Year of publication
1998
Pages
50 - 63
Database
ISI
SICI code
0167-2789(1998)112:1-2<50:ARBOTI>2.0.ZU;2-4
Abstract
The inverted pendulum with a periodic parametric forcing is considered as a bifurcation problem in the reversible setting. Parameters are gi ven by the size of the forcing and the frequency ratio. Normal form th eory provides an integrable approximation of the Poincare map generate d by a planar vector field. Genericity of the model is studied by a pe rturbation analysis, where the spatial symmetry is optional. Here equi variant singularity theory is used.