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.
Keywords:
restricted three-body problem, L4 and L5, elliptic equilibria, resonances, formal and Lie stability, exponential estimates.
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.
\Bibitem{CarPalVid20}
\by Daniela C\'arcamo-D{\'\i}az, Jes\'us F. Palaci\'an, Claudio Vidal, Patricia Yanguas
\paper On the Nonlinear Stability of the Triangular Points in the Circular Spatial Restricted Three-body Problem
\jour Regul. Chaotic Dyn.
\yr 2020
\vol 25
\issue 2
\pages 131--148
\mathnet{http://mi.mathnet.ru/rcd1055}
\crossref{https://doi.org/10.1134/S156035472002001X}
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Linking options:
https://www.mathnet.ru/eng/rcd1055
https://www.mathnet.ru/eng/rcd/v25/i2/p131
This publication is cited in the following 5 articles:
Saleem Yousuf, Ram Kishor, “Nonlinear stability of triangular equilibrium points in non-resonance case with perturbations”, Nonlinear Dyn, 112:3 (2024), 1843
Yocelyn Pérez Rothen, Claudio Vidal, “Reduction and Reconstruction of the Oscillator in 1:1:2 Resonance plus an Axially Symmetric Polynomial Perturbation”, SIAM J. Appl. Dyn. Syst., 23:3 (2024), 2489
Yocelyn Pérez Rothen, Claudio Vidal, “Reduction and reconstruction procedure of a family of polynomial Hamiltonians in 1:1:2 and 1:1:-2 resonances”, Dynamical Systems, 2024, 1
D. Carcamo-Diaz, J. F. Palacian, C. Vidal, P. Yanguas, “Nonlinear stability of elliptic equilibria in Hamiltonian systems with exponential time estimates”, Discret. Contin. Dyn. Syst., 41:11 (2021), 5183–5208
D. Carcamo-Diaz, J. F. Palacian, C. Vidal, P. Yanguas, “Nonlinear stability in the spatial attitude motion of a satellite in a circular orbit”, SIAM J. Appl. Dyn. Syst., 20:3 (2021), 1421–1463
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