Skip to main content
Log in

Periodic motions in the meridian plane of a magnetic dipole, I

  • Published:
Celestial mechanics Aims and scope Submit manuscript

    We’re sorry, something doesn't seem to be working properly.

    Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

Abstract

The six known families of symmetric simple-periodic oscillations of a charged particle in the meridian plane of an elementary magnetic dipole are now presented in a complete form. They begin and terminate by flattening on the equatorial plane of the dipole field. Three new families, consisting of asymmetric periodic oscilltaions, are discovered to branch out of the families of symmetric periodic oscillations of the open-path type.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Bray, T. A. and Goudas, C. L.: 1967,Adv. Astron. Astrophys. 5, 71.

    Google Scholar 

  • De Vogelaere, R.: 1949, Proc. Sec. Math. Congress Vancouver, p. 170.

  • De Vogelaere, R.: 1950,Can. J. Math. 2, 440.

    Google Scholar 

  • De Vogelaere, R.: 1952, Ann. Assoc. Can. Franc. Avanc. Sci., Univ. of Montreal.

  • De Vogelaere, R.: 1954,Ac. Roy. Belg. 40, 705.

    Google Scholar 

  • De Vogelaere, R.: 1958, in S. Lefschetz,Contributions to the Theory of Non-Linear Oscillations, Princeton Univ. Press, Vol. IV, p. 53.

  • Dragt, A. J.: 1965,Rev. Geophys. 3, 255.

    Google Scholar 

  • Godart, O.: 1938,Ann. Soc. Sci. Brux. 58, 27.

    Google Scholar 

  • Goudas, C., Halioulias, A., Markellos, V. and Macris, G.: 1976 in V. Szebehely and B. D. Tapley (eds.),Long-time Predictions in Dynamics.

  • Graef, C.: 1944,Bol. Soc. Matem. Mexicana 1, 1.

    Google Scholar 

  • Graef, C. and Kusaka, S.: 1938,J. Math. Phys. 17, 43.

    Google Scholar 

  • Hénon, M.: 1965,Ann. Astrophys. 28, 992.

    Google Scholar 

  • Hénon, M.: 1973,Astron. Astrophys. 28, 415.

    Google Scholar 

  • Hitzl, D. L.: 1975,Astron. Astrophys. 40, 147.

    Google Scholar 

  • Lemaître, G.: 1934,Ann. Soc. Sci. Brux. 54, 194.

    Google Scholar 

  • Lemaître, G. and Vallarta, M. S.: 1933,Phys. Rev. 43, 87.

    Google Scholar 

  • Lifshitz, J.: 1942,J. Math. Phys. 21, 284.

    Google Scholar 

  • Markellos, V.: 1974,Celest. Mech. 10, 87.

    Google Scholar 

  • Markellos, V.: 1976,Astrophys. Space Sci. 43, 449.

    Google Scholar 

  • Markellos, V. and Klimopoulos, S.: 1977,Astrophys. Space Sci. 48, 471.

    Google Scholar 

  • Markellos, V., Klimopoulos, S., and Goudas, C.: 1978,Celest. Mech. 17, 233.

    Google Scholar 

  • Mavraganis, A. and Goudas, C.: 1975,Astrophys. Space Sci. 32, 115.

    Google Scholar 

  • Schremp, E. J.: 1938,Phys. Rev. 54, 153.

    Google Scholar 

  • Störmer, C.: 1904, Vidensk. Selsk. Skriffer Christiana, No. 3, 1.

    Google Scholar 

  • Störmer, C.: 1907,Arch. Sc. Phys. Nat. 24, 113.

    Google Scholar 

  • Störmer, C.: 1930,Zeits. für Astrophys. 1, 237.

    Google Scholar 

  • Störmer, C.: 1936,Astrophys. Norveg. 2, 1.

    Google Scholar 

  • Störmer, C.: 1950, Skriffer Norske Vidensk Ak, M.N. Kl., No. 1, 5.

    Google Scholar 

  • Störmer, C.: 1955,The Polar Aurora, Clarendon Press, Oxford.

    Google Scholar 

  • Vallarta, M. S.: 1938,An Outline of The Theory of The Allowed Cone of Cosmic Radiation, Univ. of Toronto Press.

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Markellos, V.V., Klimopoulos, S. & Halioulias, A.A. Periodic motions in the meridian plane of a magnetic dipole, I. Celestial Mechanics 17, 215–232 (1978). https://doi.org/10.1007/BF01232828

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01232828

Keywords

Navigation