Results 11 to 20 of about 6,217,741 (298)
Seven-body central configurations: a family of central configurations in the spatial seven-body problem [PDF]
Celestial Mechanics and Dynamical Astronomy, 2007 The main result of this paper is the existence of a new family of central configurations in the Newtonian spatial seven-body problem. This family is unusual in that it is a simplex stacked central configuration, i.e the bodies are arranged as concentric three and two dimensional simplexes.
Marshall Hampton +2 more
exaly +3 more sources
On the centered co-circular central configurations for the n-body problem [PDF]
Journal of Differential Equations, 2022 For the power-law potential $n$-body problem, we study a special kind of central configurations where all the masses lie on a circle and the center of mass coincides with the center of the circle.
Zhiqiang Wang
semanticscholar +1 more source
On the uniqueness of trapezoidal four-body central configurations [PDF]
Nonlinearity, 2021 We study central configurations of the Newtonian four-body problem that form a trapezoid. Using a topological argument we prove that there is at most one trapezoidal central configuration for each cyclic ordering of the masses.
Manuele Santoprete
semanticscholar +1 more source
On the Uniqueness of Co-circular Four Body Central Configurations [PDF]
Archive for Rational Mechanics and Analysis, 2021 We study central configurations lying on a common circle in the Newtonian four-body problem. Using a topological argument we prove that there is at most one co-circular central configuration for each cyclic ordering of the masses on the circle.
Manuele Santoprete
semanticscholar +1 more source
RUDN Journal of Engineering Research, 2023 A hierarchical approach to proving of existence in the general (pn+1)-body exact partial solutions is presented, the so called generalized planar nested central configurations in a form of consequently nested in each other convex n -gons with nonequal in
Yulianna V. Perepelkina +1 more
doaj +1 more source
RUDN Journal of Engineering Research, 2023 The study of central configurations, whose concepts and definitions were already formulated by the classics of celestial mechanics - Euler, Lagrange, Laplace and Liouville in the XVIII-XIX centuries, is of interest not only for celestial mechanics, but ...
Yulianna V. Perepelkina +1 more
doaj +1 more source
Central configurations in the spatial n-body problem for $$n=5,6$$ with equal masses [PDF]
Celestial mechanics & dynamical astronomy, 2020 We present a computer assisted proof of the full listing of central configurations for spatialn-body problem for$$n=5$$n=5and 6, with equal masses. For each central configuration, we give a full list of its Euclidean symmetries.
M. Moczurad, P. Zgliczyński
semanticscholar +1 more source
Central Configurations in the Five-Body Problem: Rhombus Plus One
Qualitative Theory of Dynamical Systems, 2021 We show the existence of central configurations in the planar five-body problem where four bodies are located at the vertices of a rhombus, called rhombus plus one central configurations. Concretely we prove analytically their existence when one diagonal
J. Cornelio +2 more
semanticscholar +1 more source
Tangential Trapezoid Central Configurations [PDF]
Regular and Chaotic Dynamics, 2020 A tangential trapezoid, also called a circumscribed trapezoid, is a trapezoid whose four sides are all tangent to a circle within the trapezoid: the in-circle or inscribed circle. In this paper we classify all planar four-body central configurations, where the four bodies are at the vertices of a tangential trapezoid.
Yuan, Pengfei, Llibre, Jaume
openaire +4 more sources
On the Existence of Symmetric Bicircular Central Configurations of the 3n-Body Problem
Journal of nonlinear science, 2021 In this paper, we consider central configurations of the planar 3n-body problem consisting of n masses at the vertices of a regular n-gon inscribed in a circle of radius r and 2n masses at the vertices of a second (not necessarily regular) concentric 2n ...
Montserrat Corbera, C. Valls
semanticscholar +1 more source