The Kowalevski gyrostat in two constant fields is known as the unique example of
an integrable rigid body problem described by the Hamiltonian system with three
degrees of freedom not reducible to a family of systems in fewer dimensions. The
practical explicit integration of this system can hardly be obtained by the
existing techniques. Then the challenging problem becomes to fulfill the
qualitative investigation based on the study of the Liouville foliation of the
phase space. As the first approach to topological analysis of this system we
find the stratified critical set of the momentum map; this set is represented as
the union of manifolds with induced almost Hamiltonian systems having less than
three degrees of freedom. We obtain the equations of the bifurcation diagram in
three-dimensional space. These equations have the form convenient for the
classification of the bifurcation sets arising on 5-dimensional iso-energetic
levels.
Publié le : 2009-11-15
Classification:
Kowalevski gyrostat,
two constant fields,
critical set,
bifurcation diagram,
70E17,
70G40,
70H06
@article{1257544212,
author = {Kharlamov, Mikhail P.},
title = {Bifurcation diagrams and critical subsystems of the Kowalevski gyrostat in two
constant fields},
journal = {Hiroshima Math. J.},
volume = {39},
number = {1},
year = {2009},
pages = { 327-350},
language = {en},
url = {http://dml.mathdoc.fr/item/1257544212}
}
Kharlamov, Mikhail P. Bifurcation diagrams and critical subsystems of the Kowalevski gyrostat in two
constant fields. Hiroshima Math. J., Tome 39 (2009) no. 1, pp. 327-350. http://gdmltest.u-ga.fr/item/1257544212/