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Numerical exploration of commensurable periodic solutions of the restricted problem of three bodies and their stability

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Abstract

The long period problem provides the initial conditions for numerical computation of close periodic solutions separated in three categories. For each type of commensurability a number of periodic solutions are computed and their stability is studied by computing the characteristic exponents of the matrizant. The Runge-Kutta method for the solution of differential equations of motion was used in all cases. The results obtained are presented for a four cases of commensurability.

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Authors and Affiliations

  1. IBM Company, Athens, Greece

    C. N. Frangakis

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  1. C. N. Frangakis
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Frangakis, C.N. Numerical exploration of commensurable periodic solutions of the restricted problem of three bodies and their stability. Astrophys Space Sci 23, 17–42 (1973). https://doi.org/10.1007/BF00647649

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