Skip to main content
SpringerLink
Log in

Second species periodic solutions with an 0(μ) near-moon passage

  • Published:
Celestial mechanics Aims and scope Submit manuscript

Abstract

This paper uses the results of second-order asymptotic matching in the restricted three body problem to establish the existence and first-order asymptotic approximation of various families of second species periodic solutions with one near-moon passage during a half-period. In this way, the existence and asymptotic approximation of second species solutions with any number of near-moon passages during a half-period can be established based on higher order asymptotic matching. Second species solutions with near-moon passages have not been studied numerically due to the difficult nature of this problem.

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

  • Arenstorf, R. F.: 1963,Am. J. Math. 85, 27–35.

    Google Scholar 

  • Birkhoff, G. D.: 1915,Rendiconti del Circolo Matematico di Palermo 39, 265–334.

    Google Scholar 

  • Breakwell, J. V. and Perko, L. M.: 1965,Progress in Astronautics and Aeronautics 17, Academic Press, 160–180.

    Google Scholar 

  • Breakwell, J. V. and Perko, L. M.: 1974,Celes. Mech. 9, 437–450.

    Google Scholar 

  • Guillaume, P.: 1971, Doctoral dissertation, University of Liège.

  • Guillaume, P.: 1975a,Celes. Mech. 11, 213–254.

    Google Scholar 

  • Guillaume, P.: 1975b,Celes. Mech. 11, 449–467.

    Google Scholar 

  • Hénon, M.: 1968,Bull. Astron. (Paris) 3, 377–402.

    Google Scholar 

  • Perko, L. M.: 1964, Doctoral dissertation, Stanford University.

  • Perko, L. M.: 1967,Soc. Ind. Appl. Math., J. Appl. Math. 15, 738–753.

    Google Scholar 

  • Perko, L. M.: 1974,Soc. Ind. Appl. Math., J. Appl. Math. 27, 200–237.

    Google Scholar 

  • Perko, L. M.: 1976,Rocky Mountain J. Math. 6, 130–145.

    Google Scholar 

  • Poincaré, H.: 1899,Les Méthodes Nouvelles de la Méchanique Céleste, Gauthier-Villars, Paris.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Dept. of Mathematics, Northern Arizona Univ., 86001, Flagstaff, Ariz, USA

    L. M. Perko

Authors
  1. L. M. Perko
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

This research was supported in part by the National Science Foundation under Grant GP42739 and in part by Northern Arizona University under a university research grant.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Perko, L.M. Second species periodic solutions with an 0(μ) near-moon passage. Celestial Mechanics 14, 395–427 (1976). https://doi.org/10.1007/BF01229056

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01229056

Keywords

Search

Navigation