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Spatial collinear restricted four-body problem with repulsive Manev potential

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Abstract

We outline some aspects of the dynamics of an infinitesimal mass under the Newtonian attraction of three point masses in a symmetric collinear relative equilibria configuration when a repulsive Manev potential (\(-1/r +e/r^{2}\)), \(e>0\), is applied to the central mass. We investigate the relative equilibria of the infinitesimal mass and their linear stability as a function of the mass parameter \(\beta \), the ratio of mass of the central body to the mass of one of two remaining bodies, and e. We also prove the nonexistence of binary collisions between the central body and the infinitesimal mass.

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Authors and Affiliations

  1. Dept. Informàtica Matemàtica Aplicada i Estadística, Universitat de Girona, 17071, Girona, Spain

    Esther Barrabés

  2. Dept. de Matemàtiques, Universitat Politècnica de Catalunya, 08242, Manresa, Spain

    Josep M. Cors

  3. Grupo de Investigación en Sistemas Dinámicos y Aplicaciones-GISDA, Dept. de Matemática, Facultad de Ciencias, Universidad del Bío-Bío, Concepción, VIII Región, Chile

    Claudio Vidal

Authors
  1. Esther Barrabés
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  2. Josep M. Cors
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  3. Claudio Vidal
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Corresponding author

Correspondence to Esther Barrabés.

Additional information

First author is supported by the Spanish grants MTM2013-41168-P and MTM2016-80117-P (MINECO/FEDER, UE) and AGAUR grant SGR1145.

Second author is supported by MINECO grants MTM2013-40998-P, MTM2016-77278-P FEDER and AGAUR grant 2014 SGR 568.

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Barrabés, E., Cors, J.M. & Vidal, C. Spatial collinear restricted four-body problem with repulsive Manev potential. Celest Mech Dyn Astr 129, 153–176 (2017). https://doi.org/10.1007/s10569-017-9771-y

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  • DOI: https://doi.org/10.1007/s10569-017-9771-y

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