On the existence of generalised syzygies in the planar three-body problem
We consider the Newtonian planar three-body problem. One defines a generalised syzygy as a configuration where the three bodies or their velocities become collinear. Assuming that the motion is bounded and collision-free, we provide a simple sufficient condition for the existence of such configurati...
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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
Académie des sciences
2023-01-01
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| Series: | Comptes Rendus. Mathématique |
| Online Access: | https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.5802/crmath.409/ |
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| Summary: | We consider the Newtonian planar three-body problem. One defines a generalised syzygy as a configuration where the three bodies or their velocities become collinear. Assuming that the motion is bounded and collision-free, we provide a simple sufficient condition for the existence of such configurations. Our proof is elementary and uses only basic tools from the Sturm–Liouville theory. |
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| ISSN: | 1778-3569 |