The two triangular libration points of the real Earth–Moon system are not equilibrium points anymore. Under the assumption that the motion of the Moon is quasi-periodic, one special quasi-periodic orbit exists as dynamical substitute for each point. The way to compute the dynamical substitute was discussed before, and a planar approximation was obtained. In this paper, the problem is revisited. The three-dimensional approximation of the dynamical substitute is obtained in a different way. The linearized central flow around it is described.
Earth–Moon Triangular libration point Dynamical substitute Quasi-periodic orbit
This is a preview of subscription content, log in to check access
Jorba À., Ramírez R., Villanueva J.: Effective reducibility of quasi-periodic linear equations close to constant coefficients. Siam. J. Math. Anal. 28(1), 178–188 (1997)MATHCrossRefMathSciNetGoogle Scholar
Murray C.D., Dermott S.F.: Solar System Dynamics. Cambridge University Press, Cambridge (1999)MATHGoogle Scholar
Simon J.L. et al.: Numerical expressions for precession formulae and mean elements for the Moon and the planets. Astron. Astrophys. 282, 663–683 (1994)ADSGoogle Scholar
Skokos C., Dokoumetzidis A.: Effective stability of the Trojan asteroids. Astron. Astrophys. 367, 729–736 (2001)CrossRefADSGoogle Scholar
Szebehely V.: Theory of Orbits. Academic press, New York (1967)Google Scholar