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| HAL : hal-00578839, version 1 |
| arXiv : math-ph/0603075v1 |
| DOI : 10.1134/S1560354707010042 |
| Fiche détaillée |  Récupérer au format |
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| Regular and Chaotic Dynamics 12, 1 (2007) pp. 39-55 |
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| Euler configurations and quasi-polynomial systems |
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| Alain Albouy 1Yanning Fu 2 |
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| (01/2007) |
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| In the Newtonian 3-body problem, for any choice of the three masses, there are exactly three Euler configurations (also known as the three Euler points). In Helmholtz' problem of 3 point vortices in the plane, there are at most three collinear relative equilibria. The "at most three" part is common to both statements, but the respective arguments for it are usually so different that one could think of a casual coincidence. By proving a statement on a quasi-polynomial system, we show that the "at most three" holds in a general context which includes both cases. We indicate some hard conjectures about the configurations of relative equilibrium and suggest they could be attacked within the quasi-polynomial framework. |
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| 1 : | Institut de Mécanique Céleste et de Calcul des Ephémérides (IMCCE) |
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CNRS : UMR8028 – INSU – Observatoire de Paris – Université Pierre et Marie Curie [UPMC] - Paris VI – Université Lille I - Sciences et technologies |
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| 2 : | Purple Mountain Observatory |
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Purple Mountain Observatory |
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| Domaine | : | Physique/Physique mathématique Mathématiques/Physique mathématique |
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| relative equilibria – point vortex – real solutions |
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| Lien vers le texte intégral : |
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| http://fr.arXiv.org/abs/math-ph/0603075v1 |
| hal-00578839, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00578839 | |
| oai:hal.archives-ouvertes.fr:hal-00578839 | |
| Contributeur : Alain Albouy | |
| Soumis le : Mardi 22 Mars 2011, 14:29:07 | |
| Dernière modification le : Mardi 22 Mars 2011, 14:29:07 | |
