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Эта публикация цитируется в 9 научных статьях (всего в 9 статьях)
An Estimation for the Hyperbolic Region of Elliptic Lagrangian Solutions in the Planar Three-body Problem
Xijun Hu, Yuwei Ou Department of Mathematics, Shandong University, Jinan, Shandong 250100, The People’s Republic of China
Аннотация:
It is well known that the linear stability of elliptic Lagrangian solutions depends on the mass parameter $\beta=27(m_1m_2+m_2m_3+m_3m_1)/(m_1+m_2+m_3)^2 \in [0,9]$ and the eccentricity $e \in [0,1)$. Based on new techniques for evaluating the hyperbolicity and the recently developed trace formula for Hamiltonian systems [9], we identify regions for $(\beta,e)$ such that elliptic Lagrangian solutions are hyperbolic. Consequently, we have proven that the elliptic relative equilibrium of square central configurations is hyperbolic with any eccentricity.
Ключевые слова:
central configurations, elliptic relative equilibrium, linear stability, hyperbolicity, $n$-body problem.
Поступила в редакцию: 12.09.2013 Принята в печать: 16.11.2013
Образец цитирования:
Xijun Hu, Yuwei Ou, “An Estimation for the Hyperbolic Region of Elliptic Lagrangian Solutions in the Planar Three-body Problem”, Regul. Chaotic Dyn., 18:6 (2013), 732–741
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/rcd167 https://www.mathnet.ru/rus/rcd/v18/i6/p732
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