|
| | | | |
| | | |
| Stat |
Members: 3645
Articles: 2'504'928
Articles rated: 2609
25 April 2024 |
|
| | | | |
|
Article overview
| |
|
|
Phase topology of one nonclassical integrable problem of dynamics | | Pavel E. Ryabov
; | | Date: |
13 Feb 2013 | | Abstract: | We consider the integrable system with three degrees of freedom for which
Sokolov and Tsiganov specified Lax representation. Lax representation
generalizes L-A pair of the Kowalevski gyrostat in two constant fields, found
by A.G.Reyman and M.A.Semenov-Tian-Shansky. In the paper, we give the explicit
formulas for the (independent almost everywhere) additional first integrals K
and G. These integrals are functionally connected with factors of a spectral
curve of L-A pair by Sokolov and Tsiganov. Due to this form of additional
integrals K and G, without constant gyrostatic moment, we managed to find
analytically two invariant four-dimensional submanifolds on which the induced
dynamic system is almost everywhere Hamiltonian system with two degrees of
freedom. System of equations that describes one of these invariant submanifolds
is a generalization of invariant relations of an integrable Bogoyavlensky case
in dynamics of a rigid body. To describe phase topology of the system as a
whole we use the method of critical subsystems. For each subsystem, we
construct the bifurcation diagrams and specify the bifurcations of Liouville
tori both in subsystems, and in the system as a whole. | | Source: | arXiv, 1302.2976 | | Services: | Forum | Review | PDF | Favorites | |
|
|
No review found.
Did you like this article?
Note: answers to reviews or questions about the article must be posted in the forum section.
Authors are not allowed to review their own article. They can use the forum section.
browser Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)
|
| |
|
|
|
|
News, job offers and information for researchers and scientists:
| |
REGISTER