The vicinity of the Earth–Moon $$L_1$$ point in the bicircular problem
| Autor: | Àngel Jorba, Marc Jorba-Cuscó, José J. Rosales |
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| Rok vydání: | 2020 |
| Předmět: |
Lyapunov function
Physics 010504 meteorology & atmospheric sciences Applied Mathematics Infinitesimal Perturbation (astronomy) Astronomy and Astrophysics 01 natural sciences Lissajous curve Computational Mathematics symbols.namesake Pitchfork bifurcation Planar Classical mechanics Space and Planetary Science Modeling and Simulation 0103 physical sciences symbols Astrophysics::Earth and Planetary Astrophysics Halo Centre manifold 010303 astronomy & astrophysics Mathematical Physics 0105 earth and related environmental sciences |
| Zdroj: | Celestial Mechanics and Dynamical Astronomy |
| ISSN: | 1572-9478 0923-2958 |
| DOI: | 10.1007/s10569-019-9940-2 |
| Popis: | 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. |
| Databáze: | OpenAIRE |
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