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On the Nonlinear Stability of the Triangular Points in the Circular Spatial Restricted Three-body Problem

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Abstract

The well-known problem of the nonlinear stability of L4 and L5 in the circular spatial restricted three-body problem is revisited. Some new results in the light of the concept of Lie (formal) stability are presented. In particular, we provide stability and asymptotic estimates for three specific values of the mass ratio that remained uncovered. Moreover, in many cases we improve the estimates found in the literature.

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Acknowledgments

The present paper is part of the thesis of the first author [6]. The comments provided by the referees have helped us improve a first version of the paper.

Funding

The authors are partially supported by Project MTM 2017-88137-C2-1-P of the Ministry of Science, Innovation and Universities of Spain. D. Cárcamo-Díaz acknowledges support from CONICYT PhD/2016-21161143. C.Vidal is partially supported by Fondecyt grant 1180288.

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Authors and Affiliations

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

    Daniela Cárcamo-Díaz & Claudio Vidal

  2. Universidad Pública de Navarra, Departamento de Estadística, Informática y Matemáticas and Institute for Advanced Materials and Mathematics, Campus de Arrosadia, 31006, Pamplona, Spain

    Jesús F. Palacián & Patricia Yanguas

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  1. Daniela Cárcamo-Díaz
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  2. Jesús F. Palacián
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  3. Claudio Vidal
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  4. Patricia Yanguas
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Correspondence to Daniela Cárcamo-Díaz, Jesús F. Palacián, Claudio Vidal or Patricia Yanguas.

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Cárcamo-Díaz, D., Palacián, J.F., Vidal, C. et al. On the Nonlinear Stability of the Triangular Points in the Circular Spatial Restricted Three-body Problem. Regul. Chaot. Dyn. 25, 131–148 (2020). https://doi.org/10.1134/S156035472002001X

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  • DOI: https://doi.org/10.1134/S156035472002001X

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