Equilibria and stability in the restricted (n+1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$(n+1)$\end{document}-body problem with logarithm potential

被引：0

作者：

A.-M. Muscaş ^{[1
]}

Daniel Paşca ^{[2
]}

Cristina Stoica ^{[3
]}

机构：

[1] University of Oradea,The Center for Doctoral University Studies

[2] University of Oradea,Department of Mathematics and Informatics

[3] Wilfrid Laurier University,Department of Mathematics

来源：

Astrophysics and Space Science | 2025年 / 370卷 / 3期

关键词：

Logarithm potential; Restricted ; -body problem; Regular n-gon; Equilibria; Stability;

D O I：

10.1007/s10509-025-04415-w

中图分类号：

学科分类号：

摘要：

We study the existence and stability of equilibria in the regular n-gon restricted (n+1)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$(n+1)$\end{document}-body problem with logarithm potential. We determine two classes of equilibria: “infinitesimal-Eulerian” situated along lines joining the n-gon centre with a vertex (i.e. along the radii), and “infinitesimal-Lagrangian” situated on the perpendicular bisectors of the n-gon sides. The infinitesimal-Eulerian equilibria are all positioned outside the primaries n-gon and are unstable. The infinitesimal-Lagrangian equilibria appear in two families: an unstable family in the interior of the primaries’ polygon, and a linearly stable family in the exterior. We also prove the existence of an equilibrium at the centre of the polygon that is unstable.

引用