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Funktsional. Anal. i Prilozhen., 1981, Volume 15, Issue 3, Pages 54–66 (Mi faa1731)  

This article is cited in 33 scientific papers (total in 33 papers)

Periodic solutions of Kirchhoff's equations for the free motion of a rigid body in a fluid and the extended theory of Lyusternik–Shnirel'man–Morse (LSM). I

S. P. Novikov, I. Shmel'tser


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English version:
Functional Analysis and Its Applications, 1981, 15:3, 197–207

Bibliographic databases:

UDC: 517.9
Received: 08.01.1981

Citation: S. P. Novikov, I. Shmel'tser, “Periodic solutions of Kirchhoff's equations for the free motion of a rigid body in a fluid and the extended theory of Lyusternik–Shnirel'man–Morse (LSM). I”, Funktsional. Anal. i Prilozhen., 15:3 (1981), 54–66; Funct. Anal. Appl., 15:3 (1981), 197–207

Citation in format AMSBIB
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\by S.~P.~Novikov, I.~Shmel'tser
\paper Periodic solutions of Kirchhoff's equations for the free motion of a rigid body in a fluid and the extended theory of Lyusternik--Shnirel'man--Morse (LSM). I
\jour Funktsional. Anal. i Prilozhen.
\yr 1981
\vol 15
\issue 3
\pages 54--66
\mathnet{http://mi.mathnet.ru/faa1731}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=630339}
\transl
\jour Funct. Anal. Appl.
\yr 1981
\vol 15
\issue 3
\pages 197--207
\crossref{https://doi.org/10.1007/BF01089924}
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    This publication is cited in the following articles:
    1. S. P. Novikov, “Variational methods and periodic solutions of Kirchhoff-type equations. II”, Funct. Anal. Appl., 15:4 (1981), 263–274  mathnet  crossref  mathscinet  zmath  isi
    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. V. V. Kozlov, “Integrability and non-integrability in Hamiltonian mechanics”, Russian Math. Surveys, 38:1 (1983), 1–76  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    4. O. I. Bogoyavlenskii, “Integrable Euler equations on Lie algebras arising in problems of mathematical physics”, Math. USSR-Izv., 25:2 (1985), 207–257  mathnet  crossref  mathscinet  zmath
    5. V. V. Trofimov, A. T. Fomenko, “Liouville integrability of Hamiltonian systems on Lie algebras”, Russian Math. Surveys, 39:2 (1984), 1–67  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    6. S. A. Kamalin, A. M. Perelomov, “Construction of canonical coordinates on orbits of the coadjoint representation of graded Lie groups”, Funct. Anal. Appl., 18:3 (1984), 248–250  mathnet  crossref  mathscinet  zmath  isi
    7. O. I. Bogoyavlenskii, “Integrable cases of the dynamics of a rigid body, and integrable systems on the spheres $S^n$”, Math. USSR-Izv., 27:2 (1986), 203–218  mathnet  crossref  mathscinet  zmath
    8. V. V. Kozlov, “Calculus of variations in the large and classical mechanics”, Russian Math. Surveys, 40:2 (1985), 37–71  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    9. V. G. Bar'yakhtar, I. A. Leonov, T. K. Soboleva, “On the theory of periodic solutions of the stationary Landau–Lifshitz equation”, Theoret. and Math. Phys., 69:1 (1986), 1063–1065  mathnet  crossref  mathscinet  isi
    10. A. T. Fomenko, “The topology of surfaces of constant energy in integrable Hamiltonian systems, and obstructions to integrability”, Math. USSR-Izv., 29:3 (1987), 629–658  mathnet  crossref  mathscinet  zmath
    11. P. I. Holod, “Hidden symmetry of the Landau–Lifshitz equation, hierarchy of higher equations, and the dual equation for an asymmetric chiral field”, Theoret. and Math. Phys., 70:1 (1987), 11–19  mathnet  crossref  mathscinet  isi
    12. Z. A. Tevdoradze, “A remark on computation of the Arnol'd–Maslov class for Liouville tori in co-tangent bundles”, Russian Math. Surveys, 43:5 (1988), 260–261  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    13. I. A. Taimanov, “Nonselfintersecting closed extremals of multivalued or not everywhere positive functionals”, Math. USSR-Izv., 38:2 (1992), 359–374  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    14. A. V. Bolsinov, “Compatible Poisson brackets on Lie algebras and completeness of families of functions in involution”, Math. USSR-Izv., 38:1 (1992), 69–90  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    15. O. I. Bogoyavlenskii, “Euler equations on finite-dimensional Lie coalgebras, arising in problems of mathematical physics”, Russian Math. Surveys, 47:1 (1992), 117–189  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    16. I. A. Taimanov, “Closed extremals on two-dimensional manifolds”, Russian Math. Surveys, 47:2 (1992), 163–211  mathnet  crossref  mathscinet  zmath  adsnasa  isi
    17. P. V. Morozov, “The Liouville classification of integrable systems of the Clebsch case”, Sb. Math., 193:10 (2002), 1507–1533  mathnet  crossref  crossref  mathscinet  zmath  isi
    18. E. I. Yakovlev, “Bundles and Geometric Structures Associated With Gyroscopic Systems”, Journal of Mathematical Sciences, 153:6 (2008), 828–855  mathnet  crossref  mathscinet  zmath  elib
    19. 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
    20. M. Farber, D. Schütz, “Closed 1-forms in topology and dynamics”, Russian Math. Surveys, 63:6 (2008), 1079–1139  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    21. Shamolin M.V., “New cases of full integrability in dynamics of a dynamically symmetric four-dimensional solid in a nonconservative field”, Dokl. Phys., 54:3 (2009), 155–159  mathnet  crossref  mathscinet  zmath  isi
    22. M. Farber, R. Geoghegan, D. Schütz, “Closed 1-forms in topology and geometric group theory”, Russian Math. Surveys, 65:1 (2010), 143–172  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    23. 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
    24. Andrey V. Tsiganov, “New variables of separation for the Steklov–Lyapunov system”, SIGMA, 8 (2012), 012, 14 pp.  mathnet  crossref  mathscinet
    25. Salnikova T.V., “Zamknutye geodezicheskie na neodnosvyaznykh mnogoobraziyakh”, Prikladnaya matematika i mekhanika, 76:2 (2012), 233–236  elib
    26. G. E. Smirnov, “Fokusnye osobennosti v klassicheskoi mekhanike”, Nelineinaya dinam., 10:1 (2014), 101–112  mathnet
    27. A. V. Borisov, I. S. Mamaev, A. V. Tsiganov, “Non-holonomic dynamics and Poisson geometry”, Russian Math. Surveys, 69:3 (2014), 481–538  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    28. 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
    29. Iskander A. Taimanov, “On an Integrable Magnetic Geodesic Flow on the Two-torus”, Regul. Chaotic Dyn., 20:6 (2015), 667–678  mathnet  crossref  mathscinet  adsnasa
    30. Yu. A. Kordyukov, I. A. Taimanov, “Trace formula for the magnetic Laplacian”, Russian Math. Surveys, 74:2 (2019), 325–361  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    31. 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
    32. I. Yu. Polekhin, “Remarks on Forced Oscillations in Some Systems with Gyroscopic Forces”, Rus. J. Nonlin. Dyn., 16:2 (2020), 343–353  mathnet  crossref  mathscinet
    33. Yu. A. Kordyukov, I. A. Taimanov, “Quasi-classical approximation for magnetic monopoles”, Russian Math. Surveys, 75:6 (2020), 1067–1088  mathnet  crossref  crossref  mathscinet  isi  elib
  • Функциональный анализ и его приложения Functional Analysis and Its Applications
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