Advertisement

Linear stability of relative equilibria with a dominant mass

  • Richard Moeckel
Article

Abstract

A criterion for the linear stability of relative equilibria of the Newtoniann-body problem is found in the case whenn−1 of the masses are small. Several stable periodic orbits of the problem are presented as examples.

Key words

Celestial mechanics relative equilibria stability 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Andoyer, M. H. (1906). Sur les solutiones périodiques voisines des position d'équilibre relatif dans le probleme desn corps.Bull. Astron. 23, 129–146.Google Scholar
  2. 2.
    Brumberg, V. A. (1957). Permanent configurations in the problem of four bodies and their stability.Soviet Astron. 1(1), 57–79.Google Scholar
  3. 3.
    Hall, G. R. Central configurations in the planar 1+n body problem. Boston University, preprint.Google Scholar
  4. 4.
    Lagrange, J. L. (1873). Essai sur le problème des trois corps. InOuvres, Vol. 6, Gauthier-Villars, Paris.Google Scholar
  5. 5.
    Maxwell, J. C. (1890). Stability of the motion of Saturn's rings. In Niven, W. D. (ed.),The Scientific Papers of James Clerk Maxwell, Cambridge University Press, Cambridge.Google Scholar
  6. 6.
    Maxwell, J. C. (1983). Stability of the motion of Saturn's rings. In Brush, S., Everitt, C. W. F., and Garber, E. (eds.),Maxwell on Saturn's Rings, MIT Press, Cambridge, MA.Google Scholar
  7. 7.
    Meyer, K., and Hall, G. R. (1992).Introduction to Hamiltonian Dynamical Systems and the N-Body Problem, Vol. 90, Applied Mathematical Sciences, Springer, New York.Google Scholar
  8. 8.
    Pedersen, P. (1952). StabilitÄtsuntersuchung im restringierten Vierkörperproblem.Dan. Mat. Fys. Medd. 26, 16.Google Scholar
  9. 9.
    Routh, E. J. (1875). On Lapace's three particles with a supplement on the stability of their motion.Proc. Lond. Math. Soc. 6, 86–97.Google Scholar
  10. 10.
    Simó, C. (1978). Relative equuilibria of the four body problem.Cel. Mech. 18:165–184.Google Scholar

Copyright information

© Plenum Publishing Corporation 1994

Authors and Affiliations

  • Richard Moeckel
    • 1
  1. 1.School of MathematicsUniversity of MinnesotaMinneapolis

Personalised recommendations