This article is cited in 6 papers

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

Daniela Cárcamo-Díaz^a, Jesús F. Palacián^b, 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

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.

MSC: 37J25, 37N05, 70F15, 70K28

Received: 09.08.2019
Accepted: 25.01.2020

Language: English

DOI: 10.1134/S156035472002001X

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