تقرير
Two-center problem with harmonic-like interactions: periodic orbits and integrability
| العنوان: | Two-center problem with harmonic-like interactions: periodic orbits and integrability |
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| المؤلفون: | Ruiz, A. M. Escobar, Jiménez-Lara, L., Llibre, J. |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics Mathematical Physics |
| مصطلحات موضوعية: | Mathematical Physics |
| الوصف: | We study the classical planar two-center problem of a particle $m$ subjected to harmonic-like interactions with two fixed centers. For convenient values of the dimensionless parameter of this problem we use the averaging theory for showing analytically the existence of periodic orbits bifurcating from two of the three equilibrium points of the Hamiltonian system modeling this problem. Moreover, it is shown that the system is generically non-integrable in the sense of Liouville-Arnold. The analytical results are complemented by numerical computations of the Poincar\'e sections as well as providing some explicit periodic orbits. Comment: 22 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2405.15048 |
| رقم الأكسشن: | edsarx.2405.15048 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |