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Nelin. Dinam., 2015, Volume 11, Number 2, Pages 287–317 (Mi nd481)  

Original papers

Phase topology of the Kowalevski – Sokolov top

P. E. Ryabova, A. Yu. Savushkinb

a Financial University under the Government of the Russian Federation Leningradsky pr. 49, Moscow, 125993, Russia
b Russian Presidential Academy of National Economy and Public Administration ul. Gagarina 8, Volgograd, 400131, Russia

Abstract: The phase topology of the integrable Hamiltonian system on $e(3)$ found by V. V. Sokolov (2001) and generalizing the Kowalevski case is investigated. The generalization contains, along with a homogeneous potential force field, gyroscopic forces depending on the configurational variables. Relative equilibria are classified, their type is calculated and the character of stability is defined. The Smale diagrams of the case are found and the classification of iso-energy manifolds of the reduced systems with two degrees of freedom is given. The set of critical points of the complete momentum map is represented as a union of critical subsystems; each critical subsystem is a one- parameter family of almost Hamiltonian systems with one degree of freedom. For all critical points we explicitly calculate the characteristic values defining their type. We obtain the equations of the surfaces bearing the bifurcation diagram of the momentum map. We give examples of the existing iso-energy diagrams with a complete description of the corresponding rough topology (of the regular Liouville tori and their bifurcations).

Keywords: integrable Hamiltonian systems, relative equilibria, iso-energy surfaces, critical subsystems, bifurcation diagrams, rough topology

Funding Agency Grant Number
Russian Foundation for Basic Research 14-01-00119
15-41-02049


Full text: PDF file (583 kB)
References: PDF file   HTML file
UDC: 517.938.5 + 531.38
MSC: 70E05, 70E17, 37J35, 34A05
Received: 26.04.2015
Revised: 19.05.2015

Citation: P. E. Ryabov, A. Yu. Savushkin, “Phase topology of the Kowalevski – Sokolov top”, Nelin. Dinam., 11:2 (2015), 287–317

Citation in format AMSBIB
\Bibitem{RyaSav15}
\by P.~E.~Ryabov, A.~Yu.~Savushkin
\paper Phase topology of the Kowalevski\,--\,Sokolov top
\jour Nelin. Dinam.
\yr 2015
\vol 11
\issue 2
\pages 287--317
\mathnet{http://mi.mathnet.ru/nd481}


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