This article is cited in 5 scientific papers (total in 5 papers)
Topological classification of the Goryachev integrable case in rigid body dynamics
S. S. Nikolaenko
Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
A topological analysis of the Goryachev integrable case in rigid body dynamics is made on the basis of the Fomenko-Zieschang theory. The invariants (marked molecules) which are obtained give a complete description, from the standpoint of Liouville classification, of the systems of Goryachev type on various level sets
of the energy. It turns out that on appropriate energy levels the Goryachev case is Liouville equivalent to many classical integrable systems and, in particular, the Joukowski, Clebsch, Sokolov and Kovalevskaya-Yehia cases in rigid body dynamics, as well as to some integrable billiards in plane domains bounded by confocal quadrics — in other words, the foliations given by the closures of generic solutions of these systems have the same structure.
Bibliography: 15 titles.
integrable Hamiltonian system, topological classification, Liouville foliation, Goryachev case, marked molecule.
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Sbornik: Mathematics, 2016, 207:1, 113–139
MSC: Primary 37J35, 70E40; Secondary 37N10
Received: 25.03.2015 and 18.06.2015
S. S. Nikolaenko, “Topological classification of the Goryachev integrable case in rigid body dynamics”, Mat. Sb., 207:1 (2016), 123–150; Sb. Math., 207:1 (2016), 113–139
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\paper Topological classification of the Goryachev integrable case in rigid body dynamics
\jour Mat. Sb.
\jour Sb. Math.
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V. V. Vedyushkina (Fokicheva), A. T. Fomenko, “Integrable topological billiards and equivalent dynamical systems”, Izv. Math., 81:4 (2017), 688–733
S. S. Nikolaenko, “Topological classification of the Goryachev integrable systems in the rigid body dynamics: non-compact case”, Lobachevskii J. Math., 38:6 (2017), 1050–1060
I. F. Kobtsev, “Geodesic flow of a 2D ellipsoid in an elastic stress field: topological classification of solutions”, Moscow University Mathematics Bulletin, 73:2 (2018), 64–70
V. V. Vedyushkina (Fokicheva), A. T. Fomenko, “Integrable geodesic flows on orientable two-dimensional surfaces and topological billiards”, Izv. Math., 83:6 (2019), 1137–1173
I. F. Kobtsev, “An elliptic billiard in a potential force field: classification of motions, topological analysis”, Sb. Math., 211:7 (2020), 987–1013
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