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Lettere al Nuovo Cimento (1971-1985)

, Volume 7, Issue 6, pp 213–216 | Cite as

The related integral theorem in phase space: A generalization of Poisson’ theorem on constants of the motion

  • G. H. Katzin
Article

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Literatur

  1. (1).
    G. H. Katzin andJ. Levine:Journ. Math. Phys.,9, 8 (1968).MathSciNetADSCrossRefGoogle Scholar
  2. (2).
    G. H. Katzin andJ. Levine:Colloquium Mathematicum (Wroclaw),26, 21 (1972).MathSciNetMATHGoogle Scholar
  3. (3).
    G. H. Katzin:Journ. Math. Phys.,14 (1973), to appear.Google Scholar
  4. (4).
    The symbol D/dt indicates absolute differentiation with respect to the Christoffel symbols based upon the metric tensorg ij of the configuration spaceV n. Lower–case Latin indices range from 1 ton. Summation notation is used throughout.V(x) is the potential energy. Partial differentiation is indicated by a comma (,).Google Scholar
  5. (5).
    See for exampleC. W. Kilmister:Hamiltonian Dynamics (New York, 1965).Google Scholar
  6. (6).
    Upper–case Latin indices range from 1 to 2n.Google Scholar
  7. (8).
    The conditions for trajectory collineations of a conservative dynamical system were formulated in a similar manner in the configuration space formulation. Refer to ref. (3).G. H. Katzin:Journ. Math. Phys.,14 (1973), to appear.Google Scholar
  8. (9).
    K. Yano:The Theory of Lie Derivatives and Its Application (Amsterdam, 1957).Google Scholar
  9. (11).
    This theorem is the phase–space version of the related integral theorem. Refer to ref. (3)G. H. Katzin:Journ. Math. Phys.,14 (1973), to appear.Google Scholar

Copyright information

© Società Italiana di Fisica 1973

Authors and Affiliations

  • G. H. Katzin
    • 1
  1. 1.Department of PhysicsNorth Carolina State UniversityRaleigh

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