Results 1 to 10 of about 6,217,741 (298)
On central configurations of the κn-body problem [PDF]
Journal of Mathematical Analysis and Applications, 2019 We consider planar central configurations of the Newtonian κn-body problem consisting in κ groups of regular n-gons of equal masses, called ( κ , n ) -crown. We derive the equations of central configurations for a general ( κ , n ) -crown.
Esther Barrabes, Josep M Cors Iglesias
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On the equilateral pentagonal central configurations [PDF]
Communications in Nonlinear Science and Numerical Simulation, 2022 . An equilateral pentagon is a polygon in the plane with five sides of equal length. In this paper we classify the central configurations of the 5-body problem having the five bodies at the vertices of an equilateral pentagon with an axis of symmetry.
Martha Álvarez–Ramírez +2 more
semanticscholar +4 more sources
On kite central configurations [PDF]
NonlinearityWe study kite central configurations (c.c.’s) in the Newtonian four-body problem. We present a new proof that there exists a unique convex kite c.c. for a given choice of positive masses and a particular ordering of the bodies.
Gareth E. Roberts
semanticscholar +4 more sources
Stacked Central Configurations for the Spatial Nine-Body Problem [PDF]
The Scientific World Journal, 2013 We show the existence of the twisted stacked central configurations for the 9-body problem. More precisely, the position vectors x1, x2, x3, x4, and x5 are at the vertices of a square pyramid Σ; the position vectors x6, x7, x8, and x9 are at the vertices
Su Xia, Deng Chunhua
doaj +2 more sources
Trapezoid central configurations [PDF]
Applied Mathematics and Computation, 2017 We classify all planar four-body central configurations where two pairs of the bodies are on parallel lines. Using Cartesian coordinates, we show that the set of four-body trapezoid central configurations with positive masses forms a two-dimensional ...
Montserrat Corbera +3 more
semanticscholar +9 more sources
On the Symmetric Central Configurations for the Planar 1 + 4-Body Problem
Complexity, 2019 We study the planar symmetric central configurations of the 1 + 4-body problem where the symmetry axis does not contain any infinitesimal masses. Under certain assumptions, we find analytically some central configurations for suitable positive masses and
Chunhua Deng, Fengying Li, Shiqing Zhang
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Spiderweb Central Configurations [PDF]
Qualitative Theory of Dynamical Systems, 2018 In this paper we study spiderweb central configurations for the N-body problem, i.e configurations given by N=n×ℓ+1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy ...
Olivier Hénot, C. Rousseau
semanticscholar +5 more sources
Central configurations in three dimensions [PDF]
Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 2003 37 pages, 18 figures, 3 as colour jpg files. References added.
Richard Battye
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Rosette Central Configurations, Degenerate Central Configurations and Bifurcations [PDF]
Celestial Mechanics and Dynamical Astronomy, 2006 In this paper we find a class of new degenerate central configurations and bifurcations in the Newtonian $n$-body problem. In particular we analyze the Rosette central configurations, namely a coplanar configuration where $n$ particles of mass $m_1$ lie at the vertices of a regular $n$-gon, $n$ particles of mass $m_2$ lie at the vertices of another $n$-
Jinzhi Lei, Manuele Santoprete
exaly +3 more sources
Central Configurations of the Curved N-Body Problem [PDF]
Journal of Nonlinear Science, 2018 We consider the $N$-body problem of celestial mechanics in spaces of nonzero constant curvature. Using the concept of locked inertia tensor, we compute the moment of inertia for systems moving on spheres and hyperbolic spheres and show that we can recover the classical definition in the Euclidean case.
F. Diacu, C. Stoica, Shuqiang Zhu
semanticscholar +3 more sources