تقرير
Linear stability of the elliptic relative equilibria for the restricted $4$-body problem: the Euler case
| العنوان: | Linear stability of the elliptic relative equilibria for the restricted $4$-body problem: the Euler case |
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| المؤلفون: | Liu, Bowen, Zhou, Qinglong |
| سنة النشر: | 2022 |
| المجموعة: | Mathematics Mathematical Physics |
| مصطلحات موضوعية: | Mathematics - Dynamical Systems, Mathematical Physics, 70F10, 70H14, 34C25 |
| الوصف: | In this paper, we consider the elliptic relative equilibria of the restricted $4$-body problems, where the three primaries form an Euler collinear configuration and the four bodies span $\mathbf{R}^2$. We obtain the symplectic reduction to the general restricted $N$-body problem. By analyzing the relationship between this restricted $4$-body problems and the elliptic Lagrangian solutions, we obtain the linear stability of the restricted $4$-body problem by the $\omega$-Maslov index. Via numerical computations, we also obtain conditions of the stability on the mass parameters for the symmetric cases. Comment: 23 pages, 2 figures. arXiv admin note: substantial text overlap with arXiv:1907.13475; substantial text overlap with arXiv:1206.6162 by other authors |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2205.10514 |
| رقم الأكسشن: | edsarx.2205.10514 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |