Skip to main content

The stability of the triangular points in the elliptic restricted problem

Celestial mechanics volume 23, pages 89–95 (1981)Cite this article

Abstract

Results are given for the stability regions in the μ-e plane of the triangular points in the elliptic restricted three-body problem. This has been done by using the two independent second-order sets of equations, as derived by Tschauner (1971a). A new property is being used in the numerical computation, which saves up more than 50% of computer time and is also applicable to the fourth order system. One of Tschauner's (1974) transition curves (derived from analytic approximations) didn't show up here. This seems to confirm Danby's result that thee axis is a transition curve.

This is a preview of subscription content, access via your institution.

Access options

Buy single article

Instant access to the full article PDF.

39,95 €

Price includes VAT (Finland)

References

  • Alfriend, K. T. and Rand, R. H.: 1969, ‘Stability of the Triangular Points in the Elliptic Restricted Problem of Three Bodies’,AIAA J 7, 1024–1028.

    Google Scholar 

  • Bennett, A.: 1965, ‘Characteristic Exponents of the Five Equilibrium Solutions in the Elliptically Restricted Problem’,Icarus 4, 177–187.

    Google Scholar 

  • Danby, J. M. A.: 1964, ‘Stability of the Triangular Points in the Elliptic Restricted Problem of Three Bodies’,Astron. J. 69, 165–172.

    Google Scholar 

  • Hale, J. K.: 1969,Ordinary Differential Equations, Wiley-Interscience, New York, p. 267.

    Google Scholar 

  • Meire, R. and Vanderbauwhede, A.: 1979, ‘A Useful Result for Certain Linear Periodic Ordinary Differential Equations’,J. of Comput. Appl. Math.,5, 59–61.

    Google Scholar 

  • Szebehely, V.: 1967,Theory of Orbits, Academic Press, New York, 599.

    Google Scholar 

  • Tschauner, J.: 1971a, ‘Die Bewegung in der Nähe der Dreieckspunkte des Elliptischen Eingeschränkten Dreikörper-problems’,Celes. Mech.,3, 189–196.

    Google Scholar 

  • Tschauner, J.: 1971b, ‘Die Aufspaltung der Variationsgleichungen des Elliptischen Eingeschränkten Dreikörperproblems’,Celes. Mech. 3, 395–402.

    Google Scholar 

  • Tschauner, J.: 1974, ‘Die Bewegung in der Nähe der Dreieckspunkte des Elliptischen Eingeschränkten Dreikörperproblems II’,Celes. Mech. 9, 419–435.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Sterrenkundig Observatorium, Rijksuniversiteit Gent, B 9000, Gent, Belgium

    R. Meire

Authors
  1. R. Meire
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Meire, R. The stability of the triangular points in the elliptic restricted problem. Celestial Mechanics 23, 89–95 (1981). https://doi.org/10.1007/BF01228547

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01228547

Keywords

  • Numerical Computation
  • Computer Time
  • Fourth Order
  • Stability Region
  • Analytic Approximation