Abstract:
In 2001, A.V. Borisov, I.S. Mamaev, and V.V. Sokolov discovered a new integrable case on the Lie algebra so(4). This system coincides with the Poincaré equations on the Lie algebra so(4), which describe the motion of a body with cavities filled with an incompressible vortex fluid. Moreover, the Poincaré equations describe the motion of a four-dimensional gyroscope. In this paper topological properties of this system are studied. In particular, for the system under consideration the bifurcation diagrams of the momentum mapping are constructed and all Fomenko invariants are calculated. Thereby, a classification of isoenergy surfaces for this system up to the rough Liouville equivalence is obtained.
Citation:
Rasoul Akbarzadeh, Ghorbanali Haghighatdoost, “The Topology of Liouville Foliation for the Borisov–Mamaev–Sokolov Integrable Case on the Lie Algebra so(4)”, Regul. Chaotic Dyn., 20:3 (2015), 317–344
\Bibitem{AkbHag15}
\by Rasoul Akbarzadeh, Ghorbanali Haghighatdoost
\paper The Topology of Liouville Foliation for the Borisov–Mamaev–Sokolov Integrable Case on the Lie Algebra $so(4)$
\jour Regul. Chaotic Dyn.
\yr 2015
\vol 20
\issue 3
\pages 317--344
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\crossref{https://doi.org/10.1134/S1560354715030089}
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Linking options:
https://www.mathnet.ru/eng/rcd46
https://www.mathnet.ru/eng/rcd/v20/i3/p317
This publication is cited in the following 6 articles:
Vladimir Dragović, Fariba Khoshnasib-Zeinabad, “Topology of the isoenergy manifolds of the Kirchhoff rigid body case on e(3)”, Topology and its Applications, 311 (2022), 107955
R. Akbarzadeh, “The topology of isoenergetic surfaces for the Borisov–Mamaev–Sokolov integrable case on the Lie algebra so(3,1)”, Theoret. and Math. Phys., 197:3 (2018), 1727–1736
A. A. Oshemkov, P. E. Ryabov, S. V. Sokolov, “Explicit determination of certain periodic motions of a generalized two-field gyrostat”, Russ. J. Math. Phys., 24:4 (2017), 517–525
P. E. Ryabov, “Explicit integration of the system of invariant relations for the case of M. Adler and P. van Moerbeke”, Dokl. Math., 95:1 (2017), 17–20
Rasoul Akbarzadeh, “Topological Analysis Corresponding to the Borisov–Mamaev–Sokolov Integrable System on the Lie Algebra so(4)”, Regul. Chaotic Dyn., 21:1 (2016), 1–17
Pavel E. Ryabov, Andrej A. Oshemkov, Sergei V. Sokolov, “The Integrable Case of Adler – van Moerbeke. Discriminant Set and Bifurcation Diagram”, Regul. Chaotic Dyn., 21:5 (2016), 581–592
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