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Teoreticheskaya i Matematicheskaya Fizika, 2002, Volume 131, Number 2, Pages 197–205
DOI: https://doi.org/10.4213/tmf324 (Mi tmf324) 		 
This article is cited in 10 scientific papers (total in 10 papers)

Kovalevskaya Top: An Elementary Approach

A. M. Perelomov

Institute for Theoretical and Experimental Physics (Russian Federation State Scientific Center)
Full-text PDF (186 kB) Citations (10)
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DOI: https://doi.org/10.4213/tmf324
Abstract: We give an elementary, very short solution to the equations of motion for the Kovalevskaya top, using some results from the original papers by Kovalevskaya, Këtter, and Weber and also the Lax representation obtained by the author.
Received: 12.10.2001
Revised: 16.11.2001
English version:
Theoretical and Mathematical Physics, 2002, Volume 131, Issue 2, Pages 612–620
DOI: https://doi.org/10.1023/A:1015416529917
Bibliographic databases:
Language: Russian
Citation: A. M. Perelomov, “Kovalevskaya Top: An Elementary Approach”, TMF, 131:2 (2002), 197–205; Theoret. and Math. Phys., 131:2 (2002), 612–620
Citation in format AMSBIB
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\jour Theoret. and Math. Phys.
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\pages 612--620
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Linking options:
  • https://www.mathnet.ru/eng/tmf324
  • https://doi.org/10.4213/tmf324
  • https://www.mathnet.ru/eng/tmf/v131/i2/p197
    • This publication is cited in the following 10 articles:
    1. Alexei A. Deriglazov, “Improved Equations of the Lagrange Top and Examples of Analytical Solutions”, Particles, 7:3 (2024), 543  crossref
    2. Hayashi M., Shigemoto K., Tsukioka T., “Two Flows Kowalevski TOP as the Full Genus Two Jacobi'S Inversion Problem and Sp(4, R ) Lie Group Structure”, J. Phys. Commun., 6:2 (2022), 025006  crossref  isi  scopus
    3. Erik Khastyan, Sergey Krivonos, Armen Nersessian, “Euler top and freedom in supersymmetrization of one-dimensional mechanics”, Physics Letters A, 452 (2022), 128442  crossref
    4. A. V. Belyaev, “Representation of solutions to the problem of the motion of a heavy rigid body in the Kovalevskaya case in terms of Weierstrass $\zeta$- and $\wp$-functions and nonintegrability of the Hess case by quadratures”, Sb. Math., 207:7 (2016), 889–914  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    5. Kurt L., “Lax Forms and the Euler TOP Equations: a New Approach”, Ann. Phys., 327:4 (2012), 1231–1237  crossref  mathscinet  zmath  adsnasa  isi  elib  scopus  scopus
    6. Guillaumin, E, “From the Kovalevskaya to the Lagrange case in rigid body motion”, International Journal of Non-Linear Mechanics, 43:8 (2008), 794  crossref  zmath  adsnasa  isi  scopus  scopus
    7. Arango, CA, “Classical mechanics of dipolar asymmetric top molecules in collinear static electric and nonresonant linearly polarized laser fields: Energy-momentum diagrams, bifurcations and accessible configuration space”, International Journal of Bifurcation and Chaos, 18:4 (2008), 1127  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    8. Komarov, IV, “On a trajectory isomorphism of the Kowalevski gyrostat and the Clebsch problem”, Journal of Physics A-Mathematical and General, 38:13 (2005), 2917  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    9. Kuang, JL, “Homoclinic orbits of the Kovalevskaya top with perturbations”, Zamm-Zeitschrift fur Angewandte Mathematik und Mechanik, 85:4 (2005), 277  crossref  mathscinet  zmath  isi  scopus  scopus
    10. Komarov IV, Tsiganov AV, “On integration of the Kowalevski gyrostat and the Clebsch problems”, Regular & Chaotic Dynamics, 9:2 (2004), 169–187  mathnet  crossref  mathscinet  zmath  adsnasa  isi  scopus  scopus
    Citing articles in Google Scholar: Russian citations, English citations
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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