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Uspekhi Mat. Nauk, 1969, Volume 24, Issue 3(147), Pages 225–226 (Mi umn5504)  

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

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Received: 17.02.1969

Citation: V. I. Arnol'd, “The Hamiltonian nature of the Euler equations in the dynamics of a rigid body and of an ideal fluid”, Uspekhi Mat. Nauk, 24:3(147) (1969), 225–226

Citation in format AMSBIB
\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 Uspekhi Mat. Nauk
\yr 1969
\vol 24
\issue 3(147)
\pages 225--226

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    This publication is cited in the following articles:
    1. L. A. Dikii, “Hamiltonian systems connected with the rotation group”, Funct. Anal. Appl., 6:4 (1972), 326–327  mathnet  crossref  mathscinet  zmath
    2. 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
    3. A. P. Veselov, “Integrable maps”, Russian Math. Surveys, 46:5 (1991), 1–51  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. 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
    5. 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
    6. 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
    7. 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
    8. 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
    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. 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
    11. Boris Khesin, “Symplectic structures and dynamics on vortex membranes”, Mosc. Math. J., 12:2 (2012), 413–434  mathnet  crossref  mathscinet  zmath
    12. 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
    13. Levin A., Olshanetsky M., Zotov A., “Relativistic Classical Integrable Tops and Quantum R-Matrices”, J. High Energy Phys., 2014, no. 7, 012  crossref  isi
    14. 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
    15. 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
    16. 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
    17. 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
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