تقرير
Linear stability of the elliptic relative equilibria for the restricted N-body problem: two special cases
| العنوان: | Linear stability of the elliptic relative equilibria for the restricted N-body problem: two special cases |
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| المؤلفون: | Xie, Jiashengliang, Liu, Bowen, Zhou, Qinglong |
| سنة النشر: | 2023 |
| 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 $N$-body problems, where the $N-1$ primaries form an Euler-Moulton collinear central configuration or a $(1+n)$-gon central configuration. We obtain the symplectic reduction to the general restricted $N$-body problem. For the first case, by analyzing the relationship between this restricted $N$-body problems and the elliptic Lagrangian solutions, we obtain the linear stability of the restricted $N$-body problem by the $\omega$-Maslov index. Via numerical computations, we also obtain conditions of the stability on the mass parameters under $N=4$ and the symmetry of the central configuration. For the second case, there exist three positions $S_1,S_2$ and $S_3$ of the massless body (up to rotations of angle $\frac{2\pi}{n}$). For ${m_0\over m}$ sufficiently large, we show that the elliptic relative equilibria is linearly unstable if the eccentricity $0\le e |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2310.00286 |
| رقم الأكسشن: | edsarx.2310.00286 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |