Skip to main content
SpringerLink
Log in

A new regularization of the restricted three-body problem and an application

  • Published:
Celestial mechanics Aims and scope Submit manuscript

Abstract

A new regularizing transformation for the three-dimensional restricted three-body problem is constructed. It is explicitly derived and is equivalent to a simple rational map. Geometrically it is equivalent to a rotation of the 3-sphere. Unlike the KS map it is dimension preserving and is valid inn dimensions. This regularizing map is applied to the restricted problem in order to prove the existence of a family of periodic orbits which continue from a family of collision orbits.

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

  1. Moser, J.: 1970, ‘Regularization of Kepler's Problem and the Averaging Method on a Manifold’,Comm. Pure Appl. Math. 23, 609.

    Google Scholar 

  2. Belbruno, E. A.: 1979, ‘A New Regularization of the Restricted Three-Body Problem with an Application’, Ph. D. Thesis. New York University.

  3. Belbruno, E. A.: 1981, ‘A New Family of Periodic Orbits for the Restricted Problem,’Celest. Mech. 25, 195.

    Google Scholar 

  4. Albert, A.A.: 1963,Studies in Modern Algebra, Vol. 2, The Mathematical Association of America-Studies in Modern Algebra, Prentice Hall, Inc.

  5. Jacobson, F.D. and Jacobson, N.: 1949, ‘Classification and Representation of Semi-Simple Jordan Algebras,’Trans. Amer. Math. Soc. 65, 141.

    Google Scholar 

  6. Stiefel, E. L. and Schiefele, G.: 1971,Linear and Regular Celestial Mechanics, Springer-Verlag, Heidelberg.

    Google Scholar 

  7. Hall, C. T.: 1972,A Geometric Introduction to Topology, Addison-Wesley.

  8. Hopf, H.: 1974,Selecta, Springer-Verlag, Berlin.

    Google Scholar 

  9. Guillaume, P. 1974, ‘New Periodic Solutions of the Three-Dimensional Restricted Problem’,.Celest. Mech. 10, 475.

    Google Scholar 

  10. Wintner, A.: 1947,The Analytic Foundations of Celestial Mechanics, Princeton University Press.

  11. Kummer, M.: 1981, ‘On the Construction of the Reduced Phase Space of a Hamiltonian System with Symmetry’, to appear.

  12. Szebehely, V.: 1967,Theory of Orbits, Academic Press.

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Boston University, 264 Bay State Rd, 02215, Boston, Mass, USA

    E. A. Belbruno

Authors
  1. E. A. Belbruno
    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

Belbruno, E.A. A new regularization of the restricted three-body problem and an application. Celestial Mechanics 25, 397–415 (1981). https://doi.org/10.1007/BF01234179

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01234179

Keywords

Search

Navigation