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The vicinity of the Earth-Moon \(L_1\) point in the bicircular problem. (English) Zbl 1443.70040
Summary: The bicircular model is a periodic time-dependent perturbation of the Earth-Moon restricted three-body problem that includes the direct gravitational effect of the Sun on the infinitesimal particle. In this paper, we focus on the dynamics in the neighbourhood of the \(L_1\) point of the Earth-Moon system. By means of a periodic time-dependent reduction to the centre manifold, we show the existence of two families of quasi-periodic Lyapunov orbits, one planar and one vertical. The planar Lyapunov family undergoes a (quasi-periodic) pitchfork bifurcation giving rise to two families of quasi-periodic halo orbits. Between them, there is a family of Lissajous quasi-periodic orbits, with three basic frequencies.
MSC:
70F07 Three-body problems
70K60 General perturbation schemes for nonlinear problems in mechanics
37B25 Stability of topological dynamical systems
37G05 Normal forms for dynamical systems
Software:
FFTW; MPFR; Taylor
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