Chaotic dynamics in the planar gravitational many-body problem with rigid body rotations
The discovery of Pluto’s small moons in the last decade has brought attention to the dynamics of the dwarf planet’s satellites. With such systems in mind, we study a planar N-body system in which all the bodies are point masses, except for a single rigid body. We then present a reduced model consist...
| Main Authors: | , , , , |
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| Format: | Journal article |
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World Scientific Publishing
2018
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| _version_ | 1826263763554140160 |
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| author | Kwiecinski, J Kovacs, A Krause, A Planella, F Van Gorder, R |
| author_facet | Kwiecinski, J Kovacs, A Krause, A Planella, F Van Gorder, R |
| author_sort | Kwiecinski, J |
| collection | OXFORD |
| description | The discovery of Pluto’s small moons in the last decade has brought attention to the dynamics of the dwarf planet’s satellites. With such systems in mind, we study a planar N-body system in which all the bodies are point masses, except for a single rigid body. We then present a reduced model consisting of a planar N-body problem with the rigid body treated as a 1D continuum (i.e. the body is treated as a rod with an arbitrary mass distribution). Such a model provides a good approximation to highly asymmetric geometries, such as the recently observed interstellar asteroid ‘Oumuamua, but is also amenable to analysis. We analytically demonstrate the existence of homoclinic chaos in the case where one of the orbits is nearly circular by way of the Melnikov method, and give numerical evidence for chaos when the orbits are more complicated. We show that the extent of chaos in parameter space is strongly tied to the deviations from a purely circular orbit. These results suggest that chaos is ubiquitous in many-body problems when one or more of the rigid bodies exhibits nonspherical and highly asymmetric geometries. The excitation of chaotic rotations does not appear to require tidal dissipation, obliquity variation, or orbital resonance. Such dynamics give a possible explanation for routes to chaotic dynamics observed in N-body systems such as the Pluto system where some of the bodies are highly nonspherical. |
| first_indexed | 2024-03-06T19:57:01Z |
| format | Journal article |
| id | oxford-uuid:25f664c4-72b3-4cd6-8f86-75fe555d56de |
| institution | University of Oxford |
| last_indexed | 2024-03-06T19:57:01Z |
| publishDate | 2018 |
| publisher | World Scientific Publishing |
| record_format | dspace |
| spelling | oxford-uuid:25f664c4-72b3-4cd6-8f86-75fe555d56de2022-03-26T11:58:24ZChaotic dynamics in the planar gravitational many-body problem with rigid body rotationsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:25f664c4-72b3-4cd6-8f86-75fe555d56deSymplectic Elements at OxfordWorld Scientific Publishing2018Kwiecinski, JKovacs, AKrause, APlanella, FVan Gorder, RThe discovery of Pluto’s small moons in the last decade has brought attention to the dynamics of the dwarf planet’s satellites. With such systems in mind, we study a planar N-body system in which all the bodies are point masses, except for a single rigid body. We then present a reduced model consisting of a planar N-body problem with the rigid body treated as a 1D continuum (i.e. the body is treated as a rod with an arbitrary mass distribution). Such a model provides a good approximation to highly asymmetric geometries, such as the recently observed interstellar asteroid ‘Oumuamua, but is also amenable to analysis. We analytically demonstrate the existence of homoclinic chaos in the case where one of the orbits is nearly circular by way of the Melnikov method, and give numerical evidence for chaos when the orbits are more complicated. We show that the extent of chaos in parameter space is strongly tied to the deviations from a purely circular orbit. These results suggest that chaos is ubiquitous in many-body problems when one or more of the rigid bodies exhibits nonspherical and highly asymmetric geometries. The excitation of chaotic rotations does not appear to require tidal dissipation, obliquity variation, or orbital resonance. Such dynamics give a possible explanation for routes to chaotic dynamics observed in N-body systems such as the Pluto system where some of the bodies are highly nonspherical. |
| spellingShingle | Kwiecinski, J Kovacs, A Krause, A Planella, F Van Gorder, R Chaotic dynamics in the planar gravitational many-body problem with rigid body rotations |
| title | Chaotic dynamics in the planar gravitational many-body problem with rigid body rotations |
| title_full | Chaotic dynamics in the planar gravitational many-body problem with rigid body rotations |
| title_fullStr | Chaotic dynamics in the planar gravitational many-body problem with rigid body rotations |
| title_full_unstemmed | Chaotic dynamics in the planar gravitational many-body problem with rigid body rotations |
| title_short | Chaotic dynamics in the planar gravitational many-body problem with rigid body rotations |
| title_sort | chaotic dynamics in the planar gravitational many body problem with rigid body rotations |
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