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Multidimensional sleeping tops

Part of the Lecture Notes in Mathematics book series (LNM,volume 1334)

Keywords

  • Rigid Body
  • Effective Potential
  • Stationary Rotation
  • Cartan Subalgebra
  • Reduce Phase Space

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. Routh E.J., Dynamics of a system of rigid bodies.-N.Y., 1905, P.2.

    Google Scholar 

  2. Chetaev N.G., Stability of motion.-Moscow, 1965 (in Russian).

    Google Scholar 

  3. Rumyantsev V.V., Stability of permanent rotations of a heavy rigid ball.-PMM, v. 1, No. 1, 1956 (in Russian).

    Google Scholar 

  4. Arnol'd V.I., Hamiltonian character of the Euler equations describing the dynamics of a rigid body and an ideal liquid.-Usp. Matem. Nauk, 1969, v. 24, No. 3 (in Russian).

    Google Scholar 

  5. Smale S., Topology and mechanics.-Invent. Math., 1970, v.10, No.6; v.11, No.1.

    Google Scholar 

  6. Katok S.B., Supplement to the translation of Smale's article "Topology and mechanics".-Usp. Matem. Nauk, 1972, v.27, No.2 (in Russian).

    Google Scholar 

  7. Arnol'd V.I., Mathematical methods in classical mechanics.-Moscow, 1974 (in Russian).

    Google Scholar 

  8. Kuz'min P.A., Small vibrations and stability of motion.-Moscow, 1973 (in Russian).

    Google Scholar 

  9. Tatarinov Ya.V., On the study of phase topology of compact configurations with symmetry.-Vestn. MGU. Ser. Matem. Mekh., 1973, No.5 (in Russian).

    Google Scholar 

  10. Tatarinov Ya.V., Patterns of classical integrals in the problem on the rotation of a rigid body about a fixed point. Vestn. MGU. Ser. Matem. Mekh., 1974, No.6 (in Russian).

    Google Scholar 

  11. Mishchenko A.S., Integrals of geodesic flows on Lie groups.-Funkts. Analiz i ego Prilozh., 1970, v.4, No.3 (in Russian).

    Google Scholar 

  12. Manakov S.V., Comments on integration of Euler's equations for the dynamics of an n-dimensional rigid body.-Funkts. Analiz i ego Prilozh., 1976, v.10, No.10 (in Russian).

    Google Scholar 

  13. Mishchenko A,S. and Fomenko A.T., Euler's equations on finite-dimensional Lie groups.-Izv. Akad Nauk SSSR, 1978, v.42, No.2 (in Russian).

    Google Scholar 

  14. Vishik S.V. and Dolzhansky F.V., Analogues of the Euler-Poisson equations and magnetic hydrodynamics equations related to Lie groups.-Dokl. Akad. Nauk SSSR, 1978, v.238, No.5 (in Russian).

    Google Scholar 

  15. Kozlov V.V., Methods of qualitative analysis in solid state dynamics.-Moscow, 1980 (in Russian).

    Google Scholar 

  16. Fomenko A.T., Differential geometry and topology.-Moscow, 1983 (in Russian).

    Google Scholar 

  17. Kovalev A.M. and Savchenko A.Ya., Stability of stationary rotations of a rigid body about the principal axis.-PMM, 1975, v.39, No.4 (in Russian).

    Google Scholar 

  18. Sergeev V.S., On stability of permanent rotations of a heavy rigid body about a fixed axis.-PMM, 1976, v.40, No.3 (in Russian).

    Google Scholar 

  19. Chudnenko A.N., On stability of stationary rotations of a rigid body about the principal axis.-PMM, 1980, v.44, No.2 (in Russian).

    Google Scholar 

  20. Andreev D.V., On stability of permanent rotations of an asymmetric heavy rigid body.-PMM, 1983, v.47, No.3 (in Russian).

    Google Scholar 

  21. Sapronov Yu.I., Destruction of spherical symmetry in non-linear variational problems.-In: Analysis on manifolds and differential equations. Voronezh, 1986 (in Russian).

    Google Scholar 

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© 1988 Springer-Verlag

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Sapronov, Y.I. (1988). Multidimensional sleeping tops. In: Borisovich, Y.G., Gliklikh, Y.E., Vershik, A. (eds) Global Analysis — Studies and Applications III. Lecture Notes in Mathematics, vol 1334. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0080425

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  • DOI: https://doi.org/10.1007/BFb0080425

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-50019-3

  • Online ISBN: 978-3-540-45894-4

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