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Regular and Chaotic Dynamics, 2004, Volume 9, Issue 2, Pages 169–187
DOI: https://doi.org/10.1070/RD2004v009n02ABEH000274 (Mi rcd740) 		 
This article is cited in 8 scientific papers (total in 8 papers)

On integration of the Kowalevski gyrostat and the Clebsch problems

I. V. Komarov, A. V. Tsiganov

Department of Mathematical and Computational Physics V. A. Fock Institute of Physics, St. Petersburg State University, St. Petersburg, Russia
Citations (8)
DOI: https://doi.org/10.1070/RD2004v009n02ABEH000274
Abstract: For the Kowalevski gyrostat change of variables similar to that of the Kowalevski top is done. We establish one to one correspondence between the Kowalevski gyrostat and the Clebsch system and demonstrate that Kowalevski variables for the gyrostat practically coincide with elliptic coordinates on sphere for the Clebsch case. Equivalence of considered integrable systems allows to construct two Lax matrices for the gyrostat using known rational and elliptic Lax matrices for the Clebsch model. Associated with these matrices solutions of the Clebsch system and, therefore, of the Kowalevski gyrostat problem are discussed. The Kötter solution of the Clebsch system in modern notation is presented in detail.
Received: 21.06.2004
Bibliographic databases:
Document Type: Article
MSC: 37K10, 70E17, 70E40
Language: English
Citation: I. V. Komarov, A. V. Tsiganov, “On integration of the Kowalevski gyrostat and the Clebsch problems”, Regul. Chaotic Dyn., 9:2 (2004), 169–187
Citation in format AMSBIB
\Bibitem{KomTsi04}
\by I. V. Komarov, A. V. Tsiganov
\paper On integration of the Kowalevski gyrostat and the Clebsch problems
\jour Regul. Chaotic Dyn.
\yr 2004
\vol 9
\issue 2
\pages 169--187
\mathnet{http://mi.mathnet.ru/rcd740}
\crossref{https://doi.org/10.1070/RD2004v009n02ABEH000274}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2081555}
\zmath{https://zbmath.org/?q=an:1079.70514}
\adsnasa{https://adsabs.harvard.edu/cgi-bin/bib_query?2004RCD.....9..169K}
Linking options:
  • https://www.mathnet.ru/eng/rcd740
  • https://www.mathnet.ru/eng/rcd/v9/i2/p169
    • This publication is cited in the following 8 articles:
    1. Jurdjevic V., “Kowalewski TOP and Complex Lie Algebras”, Anal. Math. Phys., 11:4 (2021), 173  crossref  mathscinet  isi  scopus
    2. Borisov A. Mamaev I., “Rigid Body Dynamics”, Rigid Body Dynamics, de Gruyter Studies in Mathematical Physics, 52, Walter de Gruyter Gmbh, 2019, 1–520  mathscinet  isi
    3. Alina Dobrogowska, Tomasz Goliński, “Lie bundle on the space of deformed skew-symmetric matrices”, Journal of Mathematical Physics, 55:11 (2014)  crossref
    4. G.W. Gibbons, T. Houri, D. Kubizňák, C.M. Warnick, “Some spacetimes with higher rank Killing–Stäckel tensors”, Physics Letters B, 700:1 (2011), 68  crossref
    5. M. P. Kharlamov, “Topologicheskii analiz i bulevy funktsii: I. Metody i prilozheniya k klassicheskim sistemam”, Nelineinaya dinam., 6:4 (2010), 769–805  mathnet
    6. V. G. Marikhin, V. V. Sokolov, “Transformation of a pair of commuting Hamiltonians quadratic in momenta to canonical form and real partial separation of variables for the Clebsch top”, Regul. Chaotic Dyn., 15:6 (2010), 652–658  mathnet  crossref
    7. B. P. Tarasov, M. V. Lototskii, “Hydrogen energetics: Past, present, prospects”, Russ J Gen Chem, 77:4 (2007), 660  crossref
    8. A. V. Tsiganov, “On isomorphism of integrable cases of the Euler equations on the bi-hamiltonian manifolds $e(3)$ and $so(4)$”, J. Math. Sci. (N. Y.), 136:1 (2006), 3641–3647  mathnet  mathnet  crossref
    Citing articles in Google Scholar: Russian citations, English citations
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