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Nelin. Dinam., 2008, Volume 4, Number 4, Pages 363–407 (Mi nd244)  

This article is cited in 3 scientific papers (total in 3 papers)

The Hamiltonian dynamics of self-gravitating liquid and gas ellipsoids

A. V. Borisov, I. S. Mamaev, A. A. Kilin


Abstract: The dynamics of self-gravitating liquid and gas ellipsoids is considered. A literary survey and authors' original results obtained using modern techniques of nonlinear dynamics are presented. Strict Lagrangian and Hamiltonian formulations of the equations of motion are given; in particular, a Hamiltonian formalism based on Lie algebras is described. Problems related to nonintegrability and chaos are formulated and analyzed. All the known integrability cases are classified, and the most natural hypotheses on the nonintegrability of the equations of motion in the general case are presented. The results of numerical simulations are described. They, on the one hand, demonstrate a chaotic behavior of the system and, on the other hand, can in many cases serve as a numerical proof of the nonintegrability (the method of transversally intersecting separatrices).

Keywords: liquid and gas self-gravitating ellipsoids, integrability, chaotical behavior.

Full text: PDF file (994 kB)

Document Type: Article
Received: 03.08.2008

Citation: A. V. Borisov, I. S. Mamaev, A. A. Kilin, “The Hamiltonian dynamics of self-gravitating liquid and gas ellipsoids”, Nelin. Dinam., 4:4 (2008), 363–407

Citation in format AMSBIB
\Bibitem{BorMamKil08}
\by A.~V.~Borisov, I.~S.~Mamaev, A.~A.~Kilin
\paper The Hamiltonian dynamics of self-gravitating liquid and gas ellipsoids
\jour Nelin. Dinam.
\yr 2008
\vol 4
\issue 4
\pages 363--407
\mathnet{http://mi.mathnet.ru/nd244}


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  • http://mi.mathnet.ru/eng/nd/v4/i4/p363

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Ziglin S.L., “The Nonintegrability of the Problem on the Motion of a Homogeneous Liquid Ellipsoid”, Docl. Phys., 54:7 (2009), 348–349  mathnet  crossref  mathscinet  isi  elib  scopus
    2. S. L. Ziglin, “Ob otsutstvii dopolnitelnogo meromorfnogo pervogo integrala v zadache Rimana o dvizhenii odnorodnogo zhidkogo ellipsoida”, Nelineinaya dinam., 6:3 (2010), 567–572  mathnet
    3. I. A. Bizyaev, A. V. Borisov, I. S. Mamaev, “Figury ravnovesiya neodnorodnoi samogravitiruyuschei zhidkosti”, Nelineinaya dinam., 10:1 (2014), 73–100  mathnet
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