Skip to main content
SpringerLink
Log in

Orbits in general relativity: The Jacobian elliptic functions

Орбиты в общем теории относительности: эллиптические функции Якоби

  • Published:
Il Nuovo Cimento B (1971-1996)

Summary

The Jacobian elliptic functions are applied to the motion of monzero-rest-mass particles in the Schwarzschild geometry. The bound and unbound trajectories are analysed together with their classical and special-relativity limits.

Riassunto

Le funzioni ellittiche jacobiane sono applicate al movimento delle particelle con massa in riposo diversa da zero nella geometria di Schwarzschild. Le traiettorie legate e non legate sono analizzate insieme con i loro limiti classici e di relatività ristretta.

Резюме

Для описания движения частиц с отличной от нуля массой покоя в геометрии Шварцшильда применяются эллиптические функции Якоби. Ограниченные и неограниченные траектории анализируются вместе с их классическими пределаами и пределами в специальной теории относительности.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Y. Hagihara:Jpn. J. Astron. Geophys.,8, 67 (1931).

    MathSciNet  Google Scholar 

  2. B. Mielnik andJ. Plebanski:Acta Phys. Pol.,21, 239 (1962).

    Google Scholar 

  3. C. Darwin:Proc. R. Soc. London, Ser. A,249, 180 (1959);263, 39 (1961).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  4. A. W. Metzner:J. Math. Phys. (N. Y.),4, 1194 (1963).

    Article  MathSciNet  ADS  MATH  Google Scholar 

  5. Ya. B. Zel'dovich andJ. D. Novikov:Relativistic Astrophysics (Chicago University Press, Chicago, Ill., 1971).

    MATH  Google Scholar 

  6. S. Chandrasekhar:The Mathematical Theory of Black Holes (Oxford University Press, London, 1983).

    MATH  Google Scholar 

  7. W. Rindler:Essential Relativity, Vol.2 (Springer-Verlag, New York, N.Y. 1979).

    Google Scholar 

  8. R. M. Williams:Gen. Rel. Grav.,13, 361 (1981).

    Article  ADS  MATH  Google Scholar 

  9. W. B. Bonnor:J. Phys. A,15, 1615 (1982).

    Article  MathSciNet  ADS  Google Scholar 

  10. H. Goldstein:Classical Mechanics, 2nd edition (Addison-Wesley, Reading, Mass., 1980).

    Google Scholar 

  11. J. Díaz, A. Martín andC. Miró:J. Chem. Phys. (accepted for publication).

  12. C. W. Misner, K. S. Thorne andJ. A. Wheeler:Gravitation (Freeman, San Francisco, 1973).

    Google Scholar 

  13. H. T. Davis,Introduction to Nonlinear Differential and Integral Equations (Dover, New York, N. Y., 1962).

    MATH  Google Scholar 

  14. M. Abramowitz andI. Stegun:Handbook of Mathematical Functions (Dover, New York, N. Y., 1965).

    Google Scholar 

  15. H. Arzelies:La Dynamique relativiste et ses applications, II (Gauthier-Villars, Paris, 1958).

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departmento de Física, Facultad de Veterinaria, Universidad de Extremadura, 10071, Caceres, Spain

    C. Miró Rodríguez

Authors
  1. C. Miró Rodríguez
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Traduzione a cura della Redazione.

Переведено редакцией.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Rodríguez, C.M. Orbits in general relativity: The Jacobian elliptic functions. Nuov Cim B 98, 87–96 (1987). https://doi.org/10.1007/BF02721459

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02721459

PACS. 04.20.Jb

Search

Navigation