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Euler and mathematical methods in mechanics

  • Conference “leonhard Euler and Modern Mathematics”
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References

  1. A. N. Krylov, “Leonhard Euler,” in Collection of Works of Academician A.N. Krylov, Vol. 1, Ch. 2: Popular Scientific Works. Biographical Characteristic (Izd. Akad. Nauk SSSR, Moscow, 1951), pp. 192–217 [in Russian].

    Google Scholar 

  2. G. H. Hardy, Divergent Series (Clarendon, Oxford, 1949).

    MATH  Google Scholar 

  3. A. N. Kuznetsov, “Differentiable Solutions to Degenerate Systems of Ordinary Equations,” Funkts. Anal. Ego Prilozh. 6(2), 41–51 [Funct. Anal. Appl. 6 (2), 119–127 (1972)].

  4. A. N. Kuznetsov, “Existence of Solutions Entering at a Singular Point of an Autonomous System Having a Formal Solution,” Funkts. Anal. Ego Prilozh. 23(4), 63–74 (1989) Funct. Anal. Appl. 23 (4), 308–317 (1989).

    Google Scholar 

  5. J.-P. Ramis, Séries divergentes et théories asymptotiques, in Panoramas et Synthèses (Soc. Math. France, Paris, 1993), Vol. 121.

    MATH  Google Scholar 

  6. V. V. Kozlov, “Asymptotic Motions and the Inversion of the Lagrange-Dirichlet Theorem,” Prikl. Mat. Mekh. 50(6), 928–937 (1986) [J. Appl. Math. Mech. 50 (6), 719–725 (1986)].

    MathSciNet  Google Scholar 

  7. V. V. Kozlov and V. P. Palamodov, “On Asymptotic Solutions of the Equations of Classical Mechanics,” Dokl. Akad. Nauk SSSR 263(2), 285–289 (1982) [Soviet Math. Dokl. 25 (2), 335–339 (1982)].

    MathSciNet  Google Scholar 

  8. V. V. Kozlov and S. D. Furta, Asymptotic Expansions of Solutions of Strongly Nonlinear Systems of Differential Equations (Izd. Mosk. Univ., Moscow, 1996) [in Russian].

    MATH  Google Scholar 

  9. C. G. J. Jacobi, Vorlesungen über analytische Mechanik, in Dokumente Gesch. Math. (Deutsche Mathematiker Vereinigung, Freiburg, 1996), Vol. 8.

    Google Scholar 

  10. V. I. Arnold, “On the Topology of Three-Dimensional Steady Flows of an Ideal Fluid,” Prikl. Mat. Mekh. 30(1), 183–185 (1966) [J. Appl. Math. Mech. 30 (1), 223–226 (1966)].

    Google Scholar 

  11. V. V. Kozlov, “Notes on Steady Vortex Motions of Continuous Medium,” Prikl. Mat. Mekh. 47(2), 341–342 (1983) [J. Appl. Math. Mech. 47 (2), 288–289 (1983)].

    MathSciNet  Google Scholar 

  12. S. V. Bolotin, “Nonintegrability of the N-Center Problem for N >2,” Vestn. Mosk. Univ., Ser. 1: Mat. Mekh., No. 3, 65–68 (1984) [Moscow Univ. Mech. Bull. 39 (3), 24–28 (1984)].

  13. V. V. Kozlov, “The Hydrodynamics of Hamiltonian Systems,” Vestn. Mosk. Univ., Ser. 1: Mat. Mekh., No. 6, 10–22 (1983) [Moscow Univ. Mech. Bull. 38 (6), 9–23 (1983)].

  14. V. V. Kozlov, “An Extension of the Hamilton-Jacobi Method,” Prikl. Mat. Mekh. 60(6), 929–939 (1996) [J. Appl. Math. Mech. 60 (6), 911–920 (1996)].

    MathSciNet  Google Scholar 

  15. I. S. Arzhanykh, Momentum Fields (Nat. Lending Lib., Boston Spa, Yorkshire, 1971; Nauka, Tashkent, 1965).

    MATH  Google Scholar 

  16. V. V. Kozlov, Dynamical Systems. X. General Theory of Vortices, in Encyclopaedia Math. Sci. (Springer-Verlag, Berlin, 2003) Vol. 67.

    Google Scholar 

  17. V. V. Kozlov, “Eddy Theory of the Top,” Vestn. Mosk. Univ., Ser. 1: Mat. Mekh., No. 4, 56–62 (1990) [Moscow Univ. Mech. Bull. 45 (4), 26–38 (1990)].

  18. H. Poincaré, “Sur une forme nouvelle des équations de la m échanique,” C. R. Acad. Sci. Paris 132, 369–371 (1901).

    MATH  Google Scholar 

  19. V. V. Kozlov and V. A. Yaroshchuk, “On the Invariant Measures of Euler-Poincar é Equations on Unimodular Groups,” Vestn. Mosk. Univ., Ser. 1: Mat. Mekh., No. 2, 91–95 (1993) [Moscow Univ. Mech. Bull. 48 (2), 45–50 (1993)].

  20. J.-J. Moreau, “Une m éthode de “cin ématique fonctionnelle” en hydrodynamique,” C. R. Acad. Sci. Paris 249, 2156–2158 (1959).

    MATH  MathSciNet  Google Scholar 

  21. V. I. Yudovich, “Plane Unsteady Motion of an Ideal Incompressible Fluid,” Dokl. Akad. Nauk SSSR 136(3), 564–567 (1961) [Soviet Phys. Dokl. 6 (3), 18–20 (1961)].

    Google Scholar 

  22. V. I. Arnold, “Sur un principe variationnel pour lesécoulements stationnaires des liquides parfaits et ses applications aux problèmes de stabilité non linéaires,” J.Mécanique 5(1), 29–43 (1966).

    Google Scholar 

  23. M. V. Deryabin and Yu. N. Fedorov, “On Reductions for a Group of Geodesic Flows with (Left-) Right-Invariant Metric, and Their Symmetry Fields,” Dokl. Akad. Nauk 391(4), 439–442 (2003) [Dokl. Math. 68 (1), 75–78 (2003)].

    MathSciNet  Google Scholar 

  24. V. V. Kozlov, “Linear Systems with a Quadratic Integral,” Prikl. Mat. Mekh. 56(6), 900–906 (1992) [J. Appl. Math. Mech. 56 (6), 803–809 (1992)].

    MathSciNet  Google Scholar 

  25. V. V. Kozlov, “On the Degree of Instability,” Prikl. Mat. Mekh. 57(5), 14–19 (1993) [J. Appl. Math. Mech. 57 (5), 771–776 (1993)].

    MathSciNet  Google Scholar 

  26. A. Ostrowski and H. Schneider, “Some Theorems on the Inertia of General Matrices,” J. Math. Anal. Appl. 4(1), 72–84 (1962).

    Article  MATH  MathSciNet  Google Scholar 

  27. V. V. Kozlov, “Remarks on Eigenvalues of Real Matrices,” Dokl. Akad. Nauk 403(5), 589–592 (2005) [Dokl. Math. 72 (1), 567–569 (2005)].

    MathSciNet  Google Scholar 

  28. V. V. Kozlov and A. A. Karapetyan, “On the Degree of Stability,” Differ. Uravn. 41(2), 186–192 (2005) [Differ. Equations 41 (2), 195–201 (2005)].

    MathSciNet  Google Scholar 

  29. H. K. Wimmer, “Inertia Theorems for Matrices, Controllability, and Linear Vibrations,” Linear Algebra Appl. 8(4), 337–343 (1974).

    Article  MATH  MathSciNet  Google Scholar 

  30. P. Lancaster and M. Tismenetsky, “Inertia Characteristics of Selfajoint Matrix Polynomials,” Linear Algebra Appl. 52–53, 479–496 (1983).

    MathSciNet  Google Scholar 

  31. A. A. Shkalikov, “Operator Pencils Arising in Elasticity and Hydrodynamics: The Instability Index Formula,” in Recent Developments in Operator Theory and Its Applications. Proceedings of International Conference, Winnipeg, Canada, 1994, in Oper. Theory Adv. Appl. (Birkh äuser, Basel, 1996), Vol. 87, pp. 358–385.

    Google Scholar 

  32. Classical Dynamics in non-Euclidean Spaces, Ed. by A. V. Borisov and I. S. Mamaev (Inst. Komp’yuter. Issled., Moscow, 2004) [in Russian].

    Google Scholar 

  33. V. V. Kozlov and A. O. Harin, “Kepler’s Problem in Constant Curvature Spaces,” Celestial Mech. Dynam. Astronom. 54(4), 393–399 (1992).

    Article  MATH  MathSciNet  Google Scholar 

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Authors and Affiliations

  1. Steklov Institute of Mathematics, Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991, Russia

    V. V. Kozlov

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Original Russian Text © V.V. Kozlov, 2008, published in Sovremennye Problemy Matematiki, 2008, Vol. 11, pp. 39–70.

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Kozlov, V.V. Euler and mathematical methods in mechanics. Proc. Steklov Inst. Math. 272 (Suppl 2), 191–207 (2011). https://doi.org/10.1134/S008154381103014X

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