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Foundations of Physics

, Volume 26, Issue 3, pp 417–422 | Cite as

On general relativistic vortex-dynamics

  • Wilfried Schröder
  • Hans -Jürgen Treder
Article

Abstract

The general theory of relativity gives an absolutely covariant formulation of Helmholtz's laws of vorticity which is valid in arbitrary reference systems. For small relative velocities ui, (with ui,u′≪ε2) these generally covariant laws deliver Helmholtz's first law for a vorticity ωi in a rigidly rotating references system\(\frac{d}{{dt}}(\omega _i - \Omega _\iota ) = (\omega ^l - \Omega ^l )u_{l,i} \) with the angular velocity Ω of the rotation.

Keywords

Vorticity Angular Velocity General Theory Relative Velocity Reference System 
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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References

  1. 1.
    A. Sommerfeld,Mechanik der deformierbaren Medien, 5th edn. (Teubner, Leipzig, 1964).Google Scholar
  2. 2.
    C. Truesdell and R. A. Toupin, “The classical field theories,”Encyclopedia Physics II, I (Springer, Berlin, 1960), pp. 226–793.Google Scholar
  3. 3.
    A. Einstein,The Meaning of Relativity, 5th edn. (Princeton University Press. Princeton, 1955).Google Scholar
  4. 4.
    A. D. Fokker,Time and Space. Weight and Inertia (Pergamon, Oxford, 1960).Google Scholar
  5. 5.
    J. L. Synge,Relativity: The Special Theory, The General Theory (Kluwer, Amsterdam, 1956, 1960).Google Scholar
  6. 6.
    H. Ertel, “Analogia entre las ecuaciones del movianto y las ecuaciones del torbellino en la Hidrodinamica,”Gerlands Beitr. Geophys. 72, 312–314 (1963).Google Scholar

Copyright information

© Plenum Publishing Corporation 1996

Authors and Affiliations

  • Wilfried Schröder
    • 1
  • Hans -Jürgen Treder
    • 2
  1. 1.Bremen-RönnebeckGermany
  2. 2.PotsdamGermany

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