Skip to main content
SpringerLink
Log in

Quasiperiodic Collision Solutions in the Spatial Isosceles Three-Body Problem with Rotating Axis of Symmetry

  • Published:
Archive for Rational Mechanics and Analysis Aims and scope Submit manuscript

Abstract

We consider the spatial isosceles Newtonian three-body problem, with one particle on a fixed plane, and the other two particles (with equal masses) located symmetrically with respect to this plane. Using variational methods, we find a one-parameter family of collision solutions for this system. All these solutions are periodic in a rotating frame.

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. Albouy A., Chenciner A.: Le probléme des n corps et les distances mutuelles. Invent. Math. 131, 151–184 (1998)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  2. Chenciner A., Féjoz J., Montgomery R.: Rotating eights: I.The three Γ i families. Nonlinearity 18, 1407–1424 (2005)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  3. Fathi, A.: The Weak KAM Theorem in Lagrangian Dynamics, 2013 (in preparation)

  4. Gordon W.B.: A minimizing property of Keplerian orbits. Am. J. Math. 99(15), 961–971 (1977)

    Article  MATH  Google Scholar 

  5. Szebehely V.: Theory of Orbits. Academic Press, New York (1967)

    Google Scholar 

  6. Wintner A.: The Analytical Foundations of Celestial Mechanics. Princeton University Press, Princeton (1941)

    Google Scholar 

  7. Young L.C.: (1969), Lectures on the Calculus of Variations and Optimal Control Theory. AMS Chelsea Publishing, Providence (2000)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Departamento de Matemática, Universidade Federal de Sergipe, Av. Vereador Olímpio Grande, s/n, Sergipe, Brazil

    Eder Mateus

  2. Laboratoire d’Analyse non linéaire et gémétrie, Université d’Avignon, Avignon, France

    Andrea Venturelli

  3. Departamento de Matemática, Facultad de Ciencias, Universidad del Bío-Bío, Casilla 5-C, Concepción-VIII Región, Chile

    Claudio Vidal

Authors
  1. Eder Mateus
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Andrea Venturelli
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Claudio Vidal
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Andrea Venturelli.

Additional information

Communicated by P. Rabinowitz

The authors are partially supported by Regional Program MATH-AmSud 2009.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Mateus, E., Venturelli, A. & Vidal, C. Quasiperiodic Collision Solutions in the Spatial Isosceles Three-Body Problem with Rotating Axis of Symmetry. Arch Rational Mech Anal 210, 165–176 (2013). https://doi.org/10.1007/s00205-013-0650-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00205-013-0650-8

Keywords

Search

Navigation