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On nondegeneracy of the Hamiltonian function for a spherical pendulum

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References

  1. A. C. Clairaut, Mem. Acad. Roy. Sci., 281 (1735).

  2. Zh. Lagranzh, Analytical Mechanics (Gostekhizdat, Moscow, 1950), Vol. 2 [in Russian].

    Google Scholar 

  3. A. Tissot, J. Math. Pures et Appl. Ser. 1, 17, 88 (1852).

    Google Scholar 

  4. A. M. Lyapunov, Lecture on Theoretical Mechanics (Naukova Dumka, Kiev, 1982) [in Russian].

    Google Scholar 

  5. P. Appel’, Theoretical Mechanics (Fizmatlit, Moscow, 1960) [in Russian].

    Google Scholar 

  6. Ch.-J. Valle Poussin, Lectures on Theoretical Mechanics (Inostrannaya Literatura, Moscow, 1948), Vol. 1 [in Russian].

    Google Scholar 

  7. T. Levi-Chivita and U. Amal’di, Course of Theoretical Mechanics (Inostrannaya Literatura, Moscow, 1951), Vol. 2, Pt. 1 [in Russian].

    Google Scholar 

  8. L. A. Pars, Treatise on Analytical Dynamics (Nauka, Moscow, 1971; Wiley, New York, 1965).

    MATH  Google Scholar 

  9. V. I. Arnol’d, V. V. Kozlov, and A. I. Neĭshtadt, Mathematical Aspects of Classical and Celestial Mechanics (URSS, Moscow, 2002) [in Russian].

    Google Scholar 

  10. P. F. Byrd and M. D. Friedman, Handbook of Elliptic Integrals for Engineers and Physicists (Springer, Heidelberg, 1954).

    MATH  Google Scholar 

  11. V. Puiseux, J. Math. Pures et Appl. Ser. 1, 7, 517 (1842).

    Google Scholar 

  12. G. H. Halphen, Treatise on Elliptic Functions and Their Applications (Gauthier-Villars, Paris, 1888), Vol. 1 [in French].

    Google Scholar 

  13. A. Saint-Germain, Bull. Sci. Math. 20, 114 (1896).

    Google Scholar 

  14. A. Saint-Germain, Bull. Sci. Math. 22, 95 (1898).

    Google Scholar 

  15. I. M. Aksenenkova, Vestn. Mosk. Univ., Ser. 1, Math. Mekh., No. 1, 86 (1981).

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Authors and Affiliations

  1. Institute of Problems of Mechanics, Russian Academy of Sciences, Moscow, 117526, Russia

    A. P. Markeev

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  1. A. P. Markeev
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Original Russian Text © A.P. Markeev, 2010, published in Doklady Akademii Nauk, 2010, Vol. 430, No. 2, pp. 189–194.

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Markeev, A.P. On nondegeneracy of the Hamiltonian function for a spherical pendulum. Dokl. Phys. 55, 33–38 (2010). https://doi.org/10.1134/S1028335810010076

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  • DOI: https://doi.org/10.1134/S1028335810010076

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