Hostname: page-component-7bb8b95d7b-495rp Total loading time: 0 Render date: 2024-09-21T14:14:34.034Z Has data issue: false hasContentIssue false
  • English
  • Français

Krein Stability in the Disturbed Two-Body Problem

Published online by Cambridge University Press:  07 August 2017

R. R. Cordeiro  and
R. Vieira Martins
R. R. Cordeiro
Affiliation:
Departamento de Astronomia, Observatório Nacional, Rio de Janeiro, Brazil Departamento de Física, Universidade Federal de Viçosa, Viçosa, Brazil (permanent address)
R. Vieira Martins
Affiliation:
Departamento de Astronomia, Observatório Nacional, Rio de Janeiro, Brazil Laboratório Nacional de ComputaçÃo Científica, Rio de Janeiro, Brazil

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

We present a method for the study of the Krein signature in perturbed Hamiltonian integrable systems. The method is developed up to first order in the small parameter. We apply this method to a particular instance of the two-body problem in which the semi-major axis is not affected by the perturbation.

Keywords

Stabilityperturbationtwo-body problem
Type
Part VII - Dynamical Systems. Maps. Integrators
Information
Symposium - International Astronomical Union , Volume 152: Chaos, Resonance and Collective Dynamical Phenomena in the Solar System , 1992 , pp. 369 - 374
Copyright
Copyright © Kluwer 1992 

References

Hadjidemetriou, J. D.:(1982), Celes. Mechan. , 27, 305.Google Scholar
Hadjidemetriou, J. D.:(1985), in Resonances in the Motion of Planets, Satellites and Asteroids , Ferraz-Mello, and Sessin, eds., Universidade de São Paulo - IAG, São Paulo.Google Scholar
Hirsch, M. W.; Smale, S.:(1974), Differential Equations, Dynamical Systems, and Linear Algebra , Academic Press, New York.Google Scholar
Howard, J. E.; Mackay, R. S.:(1987), J. Math. Phys. , 28(5), 1037.CrossRefGoogle Scholar
Howard, J. E.:(1990), Celes. Mechan. Dynam Astron. , 48, 267.Google Scholar
Moser, J. K.:(1958), Commun. Pure Appl. Math. , 9, 673 CrossRefGoogle Scholar
Poincaré, H.:(1892), Les Méthodes Nouvelles de la Mécanique Céleste , Vol. 1, Gauthier-Villars et Fils, Paris.Google Scholar
Yakubovich, V.; Starzhinskii, V. M.:(1975), Linear Differential Equations with Periodics Coefficients , Vol. 1, Halsted Press, New York.Google Scholar