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Normalisation des systèmes linéaires canoniques et application au problème restreint des trois corps

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Abstract

An algorithm is given for normalizing conservative linear Hamiltonian systems. This one generalizes Siegel's method to the cases where the eigenvalues are multiple. We obtain by a canonical transformation a normal form of two blocks, one of which is the upper Jordan form, and the other, the lower Jordan form. We select real solutions from the solutions of these equations, and we apply the result to the restricted three body problem in the vicinity of the triangular points for Routh's critical mass ratio.

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Author notes

  1. Jacques Roels

    Present address: En congé de la Université de Louvain, Belgium

Authors and Affiliations

  1. University of California, Berkeley, California, U.S.A.

    Jacques Roels

  2. Université Lovanium, Léopoldville, République Démocratique du Congo

    Georges Louterman

Authors
  1. Jacques Roels
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  2. Georges Louterman
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Additional information

ℰ n est la matrice unité d'ordren,O n est la matrice nulle d'ordren.

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Roels, J., Louterman, G. Normalisation des systèmes linéaires canoniques et application au problème restreint des trois corps. Celestial Mechanics 3, 129–140 (1970). https://doi.org/10.1007/BF01230438

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  • DOI: https://doi.org/10.1007/BF01230438

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