The dynamics around the collinear points of the elliptic three-body problem: A normal form approach
Fuente:
arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915576334516224 |
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| author | Celletti, Alessandra Lhotka, Christoph Pucacco, Giuseppe |
| author_facet | Celletti, Alessandra Lhotka, Christoph Pucacco, Giuseppe |
| contents | We study the dynamics of the collinear points in the planar, restricted three-body problem, assuming that the primaries move on an elliptic orbit around a common barycenter. The equations of motion can be conveniently written in a rotating pulsating barycentric frame, taking the true anomaly as independent variable. We consider the Hamiltonian modeling this problem in the extended phase space and we imple ment a normal form to make a center manifold reduction. The normal form provides an approximate solution for the Cartesian coordinates, which allows us to construct several kinds of orbits, most notably planar and vertical Lyapunov orbits, and halo orbits. We compare the analytical results with a numerical simulation, which requires special care in the selection of the initial conditions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_21937 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The dynamics around the collinear points of the elliptic three-body problem: A normal form approach Celletti, Alessandra Lhotka, Christoph Pucacco, Giuseppe Dynamical Systems Mathematical Physics Chaotic Dynamics We study the dynamics of the collinear points in the planar, restricted three-body problem, assuming that the primaries move on an elliptic orbit around a common barycenter. The equations of motion can be conveniently written in a rotating pulsating barycentric frame, taking the true anomaly as independent variable. We consider the Hamiltonian modeling this problem in the extended phase space and we imple ment a normal form to make a center manifold reduction. The normal form provides an approximate solution for the Cartesian coordinates, which allows us to construct several kinds of orbits, most notably planar and vertical Lyapunov orbits, and halo orbits. We compare the analytical results with a numerical simulation, which requires special care in the selection of the initial conditions. |
| title | The dynamics around the collinear points of the elliptic three-body problem: A normal form approach |
| topic | Dynamical Systems Mathematical Physics Chaotic Dynamics |
| url | https://arxiv.org/abs/2510.21937 |