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Regular and Chaotic Dynamics, 2020, Volume 25, Issue 2, Pages 131–148
DOI: https://doi.org/10.1134/S156035472002001X (Mi rcd1055) 		 
This article is cited in 4 scientific papers (total in 4 papers)

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

Daniela Cárcamo-Díaza, Jesús F. Palaciánb, Claudio Vidal, Patricia Yanguas

a Universidad del Bío-Bío, Grupo de Investigación en Sistemas Dinámicos y Aplicaciones-GISDA, Departamento de Matemática, Facultad de Ciencias, Concepción, VIII Región, Chile
b Universidad Pública de Navarra, Departamento de Estadística, Informática y Matemáticas and Institute for Advanced Materials and Mathematics, Campus de Arrosadia, 31006 Pamplona, Spain
Citations (4)
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DOI: https://doi.org/10.1134/S156035472002001X
Abstract: The well-known problem of the nonlinear stability of $L_4$ and $L_5$ 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.
Keywords: restricted three-body problem, $L_4$ and $L_5$, elliptic equilibria, resonances, formal and Lie stability, exponential estimates.
Funding agency Grant number
Ministry of Science and Innovation of Spanish 2017-88137-C2-1-P
Comisión Nacional de Investigación Científica y Tecnológica PhD/2016-21161143
Fondo Nacional de Desarrollo Científico y Tecnológico 1180288
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.
Received: 09.08.2019
Accepted: 25.01.2020
Bibliographic databases:
Document Type: Article
MSC: 37J25, 37N05, 70F15, 70K28
Language: English
Citation: Daniela Cárcamo-Díaz, Jesús F. Palacián, Claudio Vidal, Patricia Yanguas, “On the Nonlinear Stability of the Triangular Points in the Circular Spatial Restricted Three-body Problem”, Regul. Chaotic Dyn., 25:2 (2020), 131–148
Citation in format AMSBIB
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\paper On the Nonlinear Stability of the Triangular Points in the Circular Spatial Restricted Three-body Problem
\jour Regul. Chaotic Dyn.
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\vol 25
\issue 2
\pages 131--148
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    References:25
     
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