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Izv. Akad. Nauk SSSR Ser. Mat., 1985, Volume 49, Issue 5, Pages 899–915 (Mi izv1370)  

This article is cited in 12 scientific papers (total in 12 papers)

Integrable cases of the dynamics of a rigid body, and integrable systems on the spheres $S^n$

O. I. Bogoyavlenskii


Abstract: Infinite-dimensional sets of integrable cases of the equations of rotation of a rigid body about a fixed point in a central force field, and also in more complicated fields (in the presence of symmetries of the inertia tensor), are found. Also considered are infinite-dimensional sets of integrable cases of the dynamics of a particle in potential fields in Euclidean space on $n$-axial ellipsoids and the spheres $S^n$.
Bibliography: 34 titles.

Full text: PDF file (1626 kB)
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English version:
Mathematics of the USSR-Izvestiya, 1986, 27:2, 203–218

Bibliographic databases:

UDC: 513.381
MSC: Primary 58F07; Secondary 58F05, 70D10, 70E15, 70H99
Received: 13.11.1984

Citation: O. I. Bogoyavlenskii, “Integrable cases of the dynamics of a rigid body, and integrable systems on the spheres $S^n$”, Izv. Akad. Nauk SSSR Ser. Mat., 49:5 (1985), 899–915; Math. USSR-Izv., 27:2 (1986), 203–218

Citation in format AMSBIB
\Bibitem{Bog85}
\by O.~I.~Bogoyavlenskii
\paper Integrable cases of the dynamics of a~rigid body, and integrable systems on the spheres~$S^n$
\jour Izv. Akad. Nauk SSSR Ser. Mat.
\yr 1985
\vol 49
\issue 5
\pages 899--915
\mathnet{http://mi.mathnet.ru/izv1370}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=810523}
\zmath{https://zbmath.org/?q=an:0616.70008}
\transl
\jour Math. USSR-Izv.
\yr 1986
\vol 27
\issue 2
\pages 203--218
\crossref{https://doi.org/10.1070/IM1986v027n02ABEH001174}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. O. I. Bogoyavlenskii, “On the question of the existence of a fourth integral of the Euler equations”, Math. USSR-Izv., 27:3 (1986), 609–609  mathnet  crossref  mathscinet  zmath
    2. A. V. Brailov, “Construction of completely integrable geodesic flows on compact symmetric spaces”, Math. USSR-Izv., 29:1 (1987), 19–31  mathnet  crossref  mathscinet  zmath
    3. A. I. Zhivkov, “Isospectral classes of matrix-valued finite-gap operators with symmetries”, Russian Math. Surveys, 44:1 (1989), 269–270  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. H M Yehia, J Phys A Math Gen, 31:27 (1998), 5819  crossref  mathscinet  zmath  adsnasa
    5. A. V. Bolsinov, V. S. Matveev, A. T. Fomenko, “Two-dimensional Riemannian metrics with integrable geodesic flows. Local and global geometry”, Sb. Math., 189:10 (1998), 1441–1466  mathnet  crossref  crossref  mathscinet  zmath  isi
    6. H M Yehia, J Phys A Math Gen, 33:33 (2000), 5945  crossref  mathscinet  zmath  adsnasa
    7. A. V. Tsyganov, “O bigamiltonovoi strukture sistem Chaplygina i Borisova–Mamaeva–Fedorova pri nulevoi konstante ploschadei. II”, Nelineinaya dinam., 8:1 (2012), 43–55  mathnet
    8. A. V. Tsiganov, “One family of conformally Hamiltonian systems”, Theoret. and Math. Phys., 173:2 (2012), 1481–1497  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib  elib
    9. A.V. Tsiganov, “On the Chaplygin system on the sphere with velocity dependent potential”, Journal of Geometry and Physics, 2015  crossref
    10. H.M. Yehia, “On the regular precession of an asymmetric rigid body acted upon by uniform gravity and magnetic fields”, Egyptian Journal of Basic and Applied Sciences, 2015  crossref
    11. A. P. Sozonov, A. V. Tsiganov, “Bäcklund transformations relating different Hamilton–Jacobi equations”, Theoret. and Math. Phys., 183:3 (2015), 768–781  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    12. Andrey V. Tsiganov, “On Integrable Perturbations of Some Nonholonomic Systems”, SIGMA, 11 (2015), 085, 19 pp.  mathnet  crossref
  • Известия Академии наук СССР. Серия математическая Izvestiya: Mathematics
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