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Analytical solution of the Lagrange quintic equation in the three-body problem in celestial mechanics

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Summary

The Lagrange equation is a quintic (fifth-degree) equation appearing in a stationary solution of the three-body problem in celestial mechanics. This equation has one positive root, which is the only required in the above problem. Here we apply an elementary real integral formula for the closed-form solution of nonlinear equations to the solution of the Lagrange equation. Two different approaches to this solution are described in detail and numerical results (obtained by both approaches) are displayed. Beyond the Lagrange equation, the present results are also applicable to the solution of other nontrivial quintic and higher-degree polynomial equations.

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Authors and Affiliations

  1. Division of Applied Mathematics and Mechanics School of Engineering, University of Patras, P. O. Box 1120, GR-261.10, Patras, Greece

    N. I. Ioakimidis & K. E. Papadakis

Authors
  1. N. I. Ioakimidis
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  2. K. E. Papadakis
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Ioakimidis, N.I., Papadakis, K.E. Analytical solution of the Lagrange quintic equation in the three-body problem in celestial mechanics. Acta Mechanica 55, 267–272 (1985). https://doi.org/10.1007/BF01175807

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  • DOI: https://doi.org/10.1007/BF01175807

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