Compactness and Index of Ordinary Central Configurations for the Curved $$N$$-Body Problem [PDF]
Regulârnaâ i haoticeskaâ dinamika, 2020 —For the curved n -body problem, we show that the set of ordinary central configurations is away from singular configurations in H 3 with positive momentum of inertia, and away from a subset of singular configurations in S 3 .
Shuqiang Zhu
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Bicentric quadrilateral central configurations [PDF]
Applied Mathematics and Computation, 2019 A bicentric quadrilateral is a tangential cyclic quadrilateral. In a tangential quadrilateral, the four sides are tangents to an inscribed circle, and in a cyclic quadrilateral the four vertices lie on a circumscribed circle. In this paper, we classify all planar central configurations of the 4-body problem, where the four bodies are at the vertices of
Jaume Llibre, Pengfei Yuan
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Equilic quadrilateral central configurations [PDF]
Communications in Nonlinear Science and Numerical Simulation, 2019 An equilic quadrilateral is a quadrilateral with one pair of opposite sides having the same length, which has angles of inclination whose sum is 2π/3. We characterize the central configurations of the 4-body problem whose four positive masses are at the vertices of equilic quadrilaterals.
Martha Alvarez-Ramírez, Jaume Llibre
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No Infinite Spin for Partial Collisions Converging to Isolated Central Configurations on the Plane [PDF]
Communications in Mathematical PhysicsIn the n-body problem, when a cluster of bodies tends to a collision, then its normalized shape curve converges to the set of normalized central configurations, which has SO(2) symmetry in the planar case.
Anna Gierzkiewicz +2 more
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On clustering in central configurations [PDF]
Proceedings of the American Mathematical Society, 1990 Central configurations lead to special solutions of the n n -body problem.
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Central configurations in planar n-body problem with equal masses for n=5,6,7\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{docu [PDF]
Celestial mechanics & dynamical astronomy, 2018 We give a computer-assisted proof of the full listing of central configuration for n-body problem for Newtonian potential on the plane for n=5,6,7\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage ...
M. Moczurad, P. Zgliczyński
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Linear stability of the elliptic relative equilibrium with (1 + n)-gon central configurations in planar n-body problem [PDF]
Nonlinearity, 2019 We study the linear stability of -gon elliptic relative equilibrium (ERE for short), that is the Kepler homographic solution with the -gon central configurations.
Xijun Hu, Y. Long, Yuwei Ou
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Classifying four-body convex central configurations [PDF]
Celestial mechanics & dynamical astronomy, 2019 We classify the full set of convex central configurations in the Newtonian planar four-body problem. Particular attention is given to configurations possessing some type of symmetry or defining geometric property.
Montserrat Corbera +2 more
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Central Configurations for Newtonian N+2p+1-Body Problems
Abstract and Applied Analysis, 2013 We show the existence of spatial central configurations for the N+2p+1-body problems. In the N+2p+1-body problems, N bodies are at the vertices of a regular N-gon T ; 2p bodies are symmetric with respect to the center of T, and located on the straight ...
Furong Zhao, Jian Chen
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Central Configurations and Action Minimizing Orbits in Kite Four-Body Problem
Advances in Astronomy, 2020 In the current article, we study the kite four-body problems with the goal of identifying global regions in the mass parameter space which admits a corresponding central configuration of the four masses.
B. Benhammouda +4 more
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