Skip to main content
SpringerLink
Log in

Stationary solutions in simplified resonance cases of the restricted three-body problem

  • Published:
Celestial mechanics Aims and scope Submit manuscript

Abstract

In the planar elliptic problem Sun-Jupiter-massless body we consider the resonances of mean motion 3/2, 2/1, 3/1, 7/3 and 1/3. Short-period effects are eliminated by Schubart's averaging method. Applying a minimization technique, stationary solutions can be found in the given resonance cases. Some of these solutions are well-known as periodic solutions in the rigorous (i.e., unaveraged) restricted problem. It is illustrated how one can construct in a numerical way a linearized theory of motion around a stationary solution and results are presented.

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

  • Bien, R.: 1978,Astron. Astrophys. 68, 295.

    Google Scholar 

  • Colombo, G., Franklin, F. A., and Munford, C. M.: 1968,Astron. J. 73, 111.

    Google Scholar 

  • Hill, G. W.: 1902,Astron. J. 22, 117.

    Google Scholar 

  • Klingman, W. R. and Himmelblau, D. M.: 1964,J. Assoc. Comput. Machinery 11, 400.

    Google Scholar 

  • Poincaré, H.: 1902,Bull. Astron. 19, 289.

    Google Scholar 

  • Schubart, J.: 1964, SAO Special Report No. 149.

  • Schubart, J.: 1966, IAU Symposium No. 25, 187.

  • Schubart, J.: 1968,Astron. J. 73, 99.

    Google Scholar 

  • Sinclair, A. T.: 1970, Monthly Notices R.A.S.148, 325.

    Google Scholar 

  • Zurmühl, R.: 1953,Praktische Mathematik, Springer-Verlag, Berlin-Göttingen-Heidelberg.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Astronomisches Rechen-Institut Heidelberg, Mönchhofstrasse 12-14, 6900, Heidelberg 1, Federal Republic of Germany

    Reinhold Bien

Authors
  1. Reinhold Bien
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Proceedings of the Sixth Conference on Mathematical Methods in Celestial Mechanics held at Oberwolfach (West Germany) from 14 to 19 August, 1978.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Bien, R. Stationary solutions in simplified resonance cases of the restricted three-body problem. Celestial Mechanics 21, 157–161 (1980). https://doi.org/10.1007/BF01230892

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01230892

Keywords

Search

Navigation