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Uspekhi Matematicheskikh Nauk, 1969, Volume 24, Issue 3(147), Pages 225–226 (Mi rm5504)  

This article is cited in 16 scientific papers (total in 17 papers)

In the Moscow Mathematical Society
Communications of the Moscow Mathematical Society

The Hamiltonian nature of the Euler equations in the dynamics of a rigid body and of an ideal fluid

V. I. Arnol'd
References:
Received: 17.02.1969
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: V. I. Arnol'd, “The Hamiltonian nature of the Euler equations in the dynamics of a rigid body and of an ideal fluid”, Russian Math. Surveys, 24:3 (1969)
Citation in format AMSBIB
\Bibitem{Arn69}
\by V.~I.~Arnol'd
\paper The Hamiltonian nature of the Euler equations in the dynamics of a~rigid body and of an ideal fluid
\jour Russian Math. Surveys
\yr 1969
\vol 24
\issue 3
\mathnet{http://mi.mathnet.ru/eng/rm5504}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=277163}
\zmath{https://zbmath.org/?q=an:0181.54204}
Linking options:
  • https://www.mathnet.ru/eng/rm5504
  • https://www.mathnet.ru/eng/rm/v24/i3/p225
  • This publication is cited in the following 17 articles:
    1. V. P. Pavlov, V. M. Sergeev, “Fluid dynamics and thermodynamics as a unified field theory”, Proc. Steklov Inst. Math., 294 (2016), 222–232  mathnet  crossref  crossref  mathscinet  isi  elib  elib
    2. Borisov A.V., Mamaev I.S., “Rigid body dynamics in non-Euclidean spaces”, Russ. J. Math. Phys., 23:4 (2016), 431–454  crossref  mathscinet  zmath  isi  scopus
    3. M. V. Shamolin, “Integrable variable dissipation systems on the tangent bundle of a multi-dimensional sphere and some applications”, J. Math. Sci., 230:2 (2018), 185–353  mathnet  crossref  elib
    4. A. M. Levin, M. A. Olshanetsky, A. V. Zotov, “Classification of isomonodromy problems on elliptic curves”, Russian Math. Surveys, 69:1 (2014), 35–118  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    5. Levin A., Olshanetsky M., Zotov A., “Relativistic Classical Integrable Tops and Quantum R-Matrices”, J. High Energy Phys., 2014, no. 7, 012  crossref  isi
    6. M. V. Shamolin, “Some classes of integrable problems in spatial dynamics of a rigid body in a nonconservative force field”, J. Math. Sci. (N. Y.), 210:3 (2015), 292–330  mathnet  crossref
    7. Boris Khesin, “Symplectic structures and dynamics on vortex membranes”, Mosc. Math. J., 12:2 (2012), 413–434  mathnet  crossref  mathscinet  zmath
    8. V. V. Trofimov, M. V. Shamolin, “Geometric and dynamical invariants of integrable Hamiltonian and dissipative systems”, J. Math. Sci., 180:4 (2012), 365–530  mathnet  crossref  mathscinet
    9. M. V. Shamolin, “Dynamical systems with variable dissipation: Approaches, methods, and applications”, J. Math. Sci., 162:6 (2009), 741–908  mathnet  crossref  mathscinet  zmath  elib  elib
    10. M. A. Olshanetsky, “Elliptic hydrodynamics and quadratic algebras of vector fields on a torus”, Theoret. and Math. Phys., 150:3 (2007), 301–314  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    11. B. M. Darinskii, Yu. I. Sapronov, S. L. Tsarev, “Bifurcations of extremals of Fredholm functionals”, Journal of Mathematical Sciences, 145:6 (2007), 5311–5453  mathnet  crossref  mathscinet  zmath  elib
    12. H. Sendra, J. E. Marsden, S. Pekarskii, T. S. Ratiu, “Variational principles for Lie–Poisson and Hamilton–Poincaré equations”, Mosc. Math. J., 3:3 (2003), 833–867  mathnet  crossref  mathscinet  zmath
    13. D. V. Anosov, A. A. Bolibrukh, V. A. Vassiliev, A. M. Vershik, A. A. Gonchar, M. L. Gromov, S. M. Gusein-Zade, V. M. Zakalyukin, Yu. S. Ilyashenko, V. V. Kozlov, M. L. Kontsevich, Yu. I. Manin, A. I. Neishtadt, S. P. Novikov, Yu. S. Osipov, M. B. Sevryuk, Ya. G. Sinai, A. N. Tyurin, L. D. Faddeev, B. A. Khesin, A. G. Khovanskii, “Vladimir Igorevich Arnol'd (on his 60th birthday)”, Russian Math. Surveys, 52:5 (1997), 1117–1139  mathnet  crossref  crossref  mathscinet  adsnasa  isi
    14. Yu. I. Sapronov, “Finite-dimensional reductions of smooth extremal problems”, Russian Math. Surveys, 51:1 (1996), 97–127  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi
    15. A. P. Veselov, “Integrable maps”, Russian Math. Surveys, 46:5 (1991), 1–51  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    16. S. P. Novikov, “The Hamiltonian formalism and a many-valued analogue of Morse theory”, Russian Math. Surveys, 37:5 (1982), 1–56  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    17. L. A. Dikii, “Hamiltonian systems connected with the rotation group”, Funct. Anal. Appl., 6:4 (1972), 326–327  mathnet  crossref  mathscinet  zmath
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Успехи математических наук Russian Mathematical Surveys
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