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The Elements of the Calculus of Variations

  • B. A. Dubrovin
  • A. T. Fomenko
  • S. P. Novikov
Part of the Graduate Texts in Mathematics book series (GTM, volume 93)

Abstract

In §29.2 we defined the geodesics x i = x i (t) relative to a given connexion Γ jk i by means of the equation
$${{\nabla }_{T}}\left( T \right) = 0$$
, where T i = dx i /dt is the velocity vector of the curve; in other words the geodesics are the solutions of the equations
$$\frac{{{d^2}{x^i}}}{{d{t^2}}} + \Gamma _{jk}^i\frac{{d{x^j}}}{{dt}}\frac{{d{x^k}}}{{dt}} = 0$$
.

Keywords

Phase Space Vector Field Hamiltonian System Poisson Bracket Canonical Transformation 
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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Copyright information

© Springer Science+Business Media New York 1984

Authors and Affiliations

  • B. A. Dubrovin
    • 1
  • A. T. Fomenko
    • 2
  • S. P. Novikov
    • 3
  1. 1.c/o VAAP-Copyright Agency of the U.S.S.R.MoscowUSSR
  2. 2.3 Ya KaracharavskayaMoscowUSSR
  3. 3.L. D. Landau Institute for Theoretical PhysicsAcademy of Sciences of the U.S.S.R.MoscowUSSR

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