Skip to main content
SpringerLink
Log in

A study of asymptotic solutions in the vicinity of the collinear libration points of the restricted three-body problem

  • Published:
Celestial mechanics Aims and scope Submit manuscript

Abstract

Some particular solutions of the restricted three-body problem which determine outgoing or incoming orbits near libration points are considered. The solutions are obtained in the form of absolutely convergent Liapounov series. It is proved that these asymptotic solutions are plane curves situated in the orbital plane of the primaries. Each family of asymptotic solutions for every collinear point consists of four solutions which are the separatrices of a saddle point. The angles of inclination of the separatrices are determined.

Резюме

Рaссмaтривaются чaстнЫе решения огрaниченной зaдaчя трех тел, aсимптотическн. приближaюуиеся или удaляющиеся от прямолинейнЫх точек либрaции. Решения полученЫ в виде бсслютхо схцящихся Ляпуновa, ⌕aсположеннЫх по степеням пноизвольной. постоянной. Покaзaно, что тaкие aсимптотиеские решени ивляются плоскими и рaсполaгaются. в плоскости двнжения основнЫх тел. Все семейство aсимптотческих решеннй дли. кaждой точки либрaции состоит из четЫрех решеннй, являющихся сепaрaтрисaми седлообрaзной. особой точки. ПолученЫ углЫ нaклонa сепaрaтрис к коордянaтнЫм осям.

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

  • Andronov, A. A., Leontovich, E. A., Gordon, I. I., and Mayer, A. G.: 1966.,The Qualitative Theory of Dynamical Systems, Nauka Moscow, Russian.

    Google Scholar 

  • Liapounov, A. M.: 1956,The Collected Works, Vol. 2, Moscow, Isdat. acad. nauk, S.S.S.R., Russ.

    Google Scholar 

  • Lukjanov, L. G.: 1976,Celes. Mech. 13, 455–464.

    Google Scholar 

  • Poincaré, H.: 1892,Les méthodes nouvelles de la mécanique céleste, t.1, Paris.

Download references

Author information

Authors and Affiliations

  1. Sternberg State Astronomical Institute, Universitetsky prospect, 13, V-234, Moscow, U.S.S.R.

    L. G. Lukjanov

Authors
  1. L. G. Lukjanov
    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

Lukjanov, L.G. A study of asymptotic solutions in the vicinity of the collinear libration points of the restricted three-body problem. Celestial Mechanics 15, 489–500 (1977). https://doi.org/10.1007/BF01228614

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01228614

Keywords

Search

Navigation