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Theoretical and Mathematical Physics

, Volume 153, Issue 1, pp 1364–1372 | Cite as

Dynamical principle

  • V. P. PavlovEmail author
  • V. M. Sergeev
Article

Abstract

We suggest a formulation of the dynamical principle for mechanics in which time is not a preferred evolution parameter but plays the role of a new generalized coordinate. The advantage of this approach is the possibility of extending it to dynamical systems in which there is no natural evolution parameter (thermodynamics, equilibrium economics, and the like).

Keywords

dynamical system variational principle Cartan-Liouville form symplectic structure 

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References

  1. 1.
    P. A. M. Dirac, Proc. Roy. Soc. London. Ser. A, 246, 326–332 (1958).zbMATHADSMathSciNetCrossRefGoogle Scholar
  2. 2.
    L. D. Faddeev, Theor. Math. Phys., 1, 1–13 (1969).CrossRefMathSciNetGoogle Scholar
  3. 3.
    A. M. Vershik and L. D. Faddeev, Soviet Phys. Dokl., 17, 34–36 (1972).zbMATHADSGoogle Scholar
  4. 4.
    V. P. Pavlov and A. O. Starinetz, Theor. Math. Phys., 105, 1539–1545 (1995).zbMATHCrossRefGoogle Scholar
  5. 5.
    V. V. Kozlov, Thermal Equilibrium per Gibbs and Poincaré [in Russian], Institut Komp’yuternykh Issledovanij, Moscow (2002).Google Scholar
  6. 6.
    V. M. Sergeev, Limits of Rationality: Thermodynamic Approach to the Theory of Economic Equilibrium [in Russian], FAZIS, Moscow (1999).Google Scholar
  7. 7.
    C. Godbillon, Géométrie différentielle et mécanique analytique, Hermann, Paris (1969).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2007

Authors and Affiliations

  1. 1.Steklov Mathematical InstituteRASMoscowRussia
  2. 2.Moscow State Institute of International RelationsCenter for Studying Global ProblemsMoscowRussia

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