Skip to main content
Log in

A compact model for the planar rhomboidal 4-body problem

  • Published:
Celestial Mechanics and Dynamical Astronomy Aims and scope Submit manuscript

Abstract

We obtain a compact model for the global study of the planar rhomboidal 4-body problem in a level of constant negative energy. This model is a variation of the non compact model obtained through a McGehee blow up transformation. but compactness permits to obtain results which are not clear in the other case.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Delgado J. and Pérez-Chavela E.: 1991, ‘The rhomboidal four body problem. Global flow on the total collision manifold’, in T. Ratiu (ed.), The Hamiltonian Systems. MSRI Series. Vol. 22, Springer-Verlag, pp. 97–110.

  2. Devaney, R.: 1981, ‘Singularities in classical mechanical systems’. in A. Katok (ed.), Ergodic Theory and Dynamical Systems, Vol. I. Birkhauser, Basel, pp. 211–333.

    Google Scholar 

  3. Forsyth, A. R.: 1900. Theory of Differential Equations, Vol. III. Cambridge University Press.

  4. McGehee, R.: 1974, ‘Triple collision in the collinear three-body problem’, Inventiones Math. 27, 191–227.

    Google Scholar 

  5. Saari, D.: 1973. ‘Singularities and collisions of Newtonian gravitational systems’, Arch. Rational Mech. Anal. 49, 311–320.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Rights and permissions

Reprints and permissions

About this article

Cite this article

Lacomba, E.A., Pérez-Chavela, E. A compact model for the planar rhomboidal 4-body problem. Celestial Mech Dyn Astr 54, 343–355 (1992). https://doi.org/10.1007/BF00049146

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF00049146

Key words

Navigation