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This article is cited in 6 scientific papers (total in 6 papers)
The Topology of Liouville Foliation for the Borisov–Mamaev–Sokolov Integrable Case on the Lie Algebra $so(4)$
Rasoul Akbarzadeh, Ghorbanali Haghighatdoost Azarbaijan Shahid Madani University, 35 Km Tabriz-Maragheh Road, Tabriz, Iran
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.
Keywords:
integrable Hamiltonian systems, isoenergy surfaces, Kirchhoff equations, Liouville foliation, bifurcation diagram, Borisov–Mamaev–Sokolov case, topological invariant.
Received: 06.03.2015
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
Linking options:
https://www.mathnet.ru/eng/rcd46 https://www.mathnet.ru/eng/rcd/v20/i3/p317
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