|
Special Issue: On the 80th birthday of professor A. Chenciner
Linear Stability of an Elliptic Relative Equilibrium in the Spatial $n$-Body Problem via Index Theory
Xijun Hu, Yuwei Ou, Xiuting Tang School of Mathematics, Shandong University,
250100 Jinan, Shandong, The People’s Republic of China
Аннотация:
It is well known that a planar central configuration of the $n$-body problem gives rise to a solution where each
particle moves in a Keplerian orbit with a common eccentricity $\mathfrak{e}\in[0,1)$. We call
this solution an elliptic
relative equilibrium (ERE for short). Since each particle of the ERE is always in the same
plane, it is natural to regard
it as a planar $n$-body problem. But in practical applications, it is more meaningful to
consider the ERE as a spatial $n$-body problem (i. e., each particle belongs to $\mathbb{R}^3$).
In this paper, as a spatial $n$-body problem, we first decompose the linear system of ERE into
two parts, the planar and the spatial part.
Following the Meyer – Schmidt coordinate [19], we give an expression for the spatial part and
further obtain a rigorous analytical method to study the linear stability of
the spatial part by the Maslov-type index theory. As an application, we obtain stability results for some classical ERE, including the
elliptic Lagrangian solution, the Euler solution and the $1+n$-gon solution.
Ключевые слова:
linear stability, elliptic relative equilibrium, Maslov-type index, spatial $n$-body problem.
Поступила в редакцию: 11.04.2023 Принята в печать: 14.07.2023
Образец цитирования:
Xijun Hu, Yuwei Ou, Xiuting Tang, “Linear Stability of an Elliptic Relative Equilibrium in the Spatial $n$-Body Problem via Index Theory”, Regul. Chaotic Dyn., 28:4-5 (2023), 731–755
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/rcd1230 https://www.mathnet.ru/rus/rcd/v28/i4/p731
|
Статистика просмотров: |
Страница аннотации: | 33 | Список литературы: | 12 |
|