Two Periodic Models for the Earth-Moon System
This paper discusses two alternative models to the Restricted Three Body Problem (RTBP) for the motion of a massless particle in the Earth-Moon system. These models are the Bicircular Problem (BCP) and the Quasi-Bicircular Problem (QBCP). While the RTBP is autonomous, the BCP and the QBCP are period...
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| Format: | Article |
| Language: | English |
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Frontiers Media S.A.
2018-07-01
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| Series: | Frontiers in Applied Mathematics and Statistics |
| Subjects: | |
| Online Access: | https://www.frontiersin.org/article/10.3389/fams.2018.00032/full |
| _version_ | 1818930209800323072 |
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| author | Marc Jorba-Cuscó Ariadna Farrés Àngel Jorba |
| author_facet | Marc Jorba-Cuscó Ariadna Farrés Àngel Jorba |
| author_sort | Marc Jorba-Cuscó |
| collection | DOAJ |
| description | This paper discusses two alternative models to the Restricted Three Body Problem (RTBP) for the motion of a massless particle in the Earth-Moon system. These models are the Bicircular Problem (BCP) and the Quasi-Bicircular Problem (QBCP). While the RTBP is autonomous, the BCP and the QBCP are periodically time dependent due to the inclusion of the Sun's gravitational potential. Each of the two alternative models is suitable for certain regions of the phase space. More concretely, we show that the BCP is more adequate to study the dynamics near the triangular points while the QBCP is more adequate for the dynamics near the collinear points. |
| first_indexed | 2024-12-20T03:57:04Z |
| format | Article |
| id | doaj.art-968eecc64b10482eb27442634ea19d75 |
| institution | Directory Open Access Journal |
| issn | 2297-4687 |
| language | English |
| last_indexed | 2024-12-20T03:57:04Z |
| publishDate | 2018-07-01 |
| publisher | Frontiers Media S.A. |
| record_format | Article |
| series | Frontiers in Applied Mathematics and Statistics |
| spelling | doaj.art-968eecc64b10482eb27442634ea19d752022-12-21T19:54:16ZengFrontiers Media S.A.Frontiers in Applied Mathematics and Statistics2297-46872018-07-01410.3389/fams.2018.00032392773Two Periodic Models for the Earth-Moon SystemMarc Jorba-Cuscó0Ariadna Farrés1Àngel Jorba2Departament de Matemàtiques i Informàtica, Universitat de Barcelona, Barcelona, SpainGoddard Planetary Heliophysics Institute, University of Maryland Baltimore Country, Baltimore, MD, United StatesDepartament de Matemàtiques i Informàtica, Universitat de Barcelona, Barcelona, SpainThis paper discusses two alternative models to the Restricted Three Body Problem (RTBP) for the motion of a massless particle in the Earth-Moon system. These models are the Bicircular Problem (BCP) and the Quasi-Bicircular Problem (QBCP). While the RTBP is autonomous, the BCP and the QBCP are periodically time dependent due to the inclusion of the Sun's gravitational potential. Each of the two alternative models is suitable for certain regions of the phase space. More concretely, we show that the BCP is more adequate to study the dynamics near the triangular points while the QBCP is more adequate for the dynamics near the collinear points.https://www.frontiersin.org/article/10.3389/fams.2018.00032/fullRestricted Three Body ProblemBicircular ProblemQuasi-Bicircular Problemperiodic hamiltonianstroboscopic mapinvariant manifolds |
| spellingShingle | Marc Jorba-Cuscó Ariadna Farrés Àngel Jorba Two Periodic Models for the Earth-Moon System Frontiers in Applied Mathematics and Statistics Restricted Three Body Problem Bicircular Problem Quasi-Bicircular Problem periodic hamiltonian stroboscopic map invariant manifolds |
| title | Two Periodic Models for the Earth-Moon System |
| title_full | Two Periodic Models for the Earth-Moon System |
| title_fullStr | Two Periodic Models for the Earth-Moon System |
| title_full_unstemmed | Two Periodic Models for the Earth-Moon System |
| title_short | Two Periodic Models for the Earth-Moon System |
| title_sort | two periodic models for the earth moon system |
| topic | Restricted Three Body Problem Bicircular Problem Quasi-Bicircular Problem periodic hamiltonian stroboscopic map invariant manifolds |
| url | https://www.frontiersin.org/article/10.3389/fams.2018.00032/full |
| work_keys_str_mv | AT marcjorbacusco twoperiodicmodelsfortheearthmoonsystem AT ariadnafarres twoperiodicmodelsfortheearthmoonsystem AT angeljorba twoperiodicmodelsfortheearthmoonsystem |