scholarly journals Spatial Central Configurations with Two Twisted Regular 4-Gons

2013 ◽  
Vol 2013 ◽  
pp. 1-6
Author(s):  
Sen Zhang ◽  
Furong Zhao
Keyword(s):  
Twist Angle ◽  
Central Configurations ◽  
Central Configuration ◽  
Spatial Central Configurations ◽  
The Masses ◽  
Axis Passing

We study the configuration formed by two squares in two parallel layers separated by a distance. We picture the two layers horizontally with thez-axis passing through the centers of the two squares. The masses located on the vertices of each square are equal, but we do not assume that the masses of the top square are equal to the masses of the bottom square. We prove that the above configuration of two squares forms a central configuration if and only if the twist angle is equal tokπ/2or (π/4+kπ/2)(k=1,2,3,4).

scholarly journals Central Configurations for NewtonianN+2p+1-Body Problems

2013 ◽  
Vol 2013 ◽  
pp. 1-5
Author(s):  
Furong Zhao ◽  
Jian Chen
Keyword(s):  
Central Configurations ◽  
Straight Line ◽  
Spatial Central Configurations ◽  
The Masses

We show the existence of spatial central configurations for theN+2p+1-body problems. In theN+2p+1-body problems,Nbodies are at the vertices of a regularN-gonT;2pbodies are symmetric with respect to the center ofT, and located on the straight line which is perpendicular to the regularN-gonTand passes through the center ofT; theN+2p+1th is located at the the center ofT. The masses located on the vertices of the regularN-gon are assumed to be equal; the masses located on the same line and symmetric with respect to the center ofTare equal.

scholarly journals Symmetry of planar four-body convex central configurations

2008 ◽  
Vol 464 (2093) ◽  
pp. 1355-1365 ◽  
Author(s):  
Alain Albouy ◽  
Yanning Fu ◽  
Shanzhong Sun
Keyword(s):  
Body Problem ◽  
The Other ◽  
Central Configurations ◽  
Central Configuration ◽  
Geometric Properties ◽  
Four Body Problem ◽  
Planar Central Configurations ◽  
The Masses ◽  
The Relationship ◽  
Convex Central Configuration

We study the relationship between the masses and the geometric properties of central configurations. We prove that, in the planar four-body problem, a convex central configuration is symmetric with respect to one diagonal if and only if the masses of the two particles on the other diagonal are equal. If these two masses are unequal, then the less massive one is closer to the former diagonal. Finally, we extend these results to the case of non-planar central configurations of five particles.

scholarly journals Regions of Central Configurations in a Symmetric 4 + 1-Body Problem

2015 ◽  
Vol 2015 ◽  
pp. 1-11 ◽  
Author(s):  
Muhammad Shoaib
Keyword(s):  
Inverse Problem ◽  
Body Problem ◽  
Center Of Mass ◽  
Central Configurations ◽  
Central Configuration ◽  
Isosceles Trapezoid ◽  
The Masses

The inverse problem of central configuration of the trapezoidal 5-body problems is investigated. In this 5-body setup, one of the masses is chosen to be stationary at the center of mass of the system and four-point masses are placed on the vertices of an isosceles trapezoid with two equal massesm1=m4at positions∓0.5, rBandm2=m3at positions∓α/2,rA. The regions of central configurations where it is possible to choose positive masses are derived both analytically and numerically. It is also shown that in the complement of these regions no central configurations are possible.

scholarly journals On the Existence of Central Configurations of2k+2p+2l-Body Problems

2014 ◽  
Vol 2014 ◽  
pp. 1-5 ◽  
Author(s):  
Yueyong Jiang ◽  
Furong Zhao
Keyword(s):  
Central Configurations ◽  
The Masses

We prove the existence of central configurations of the2k+2p+2l-body problems with Newtonian potentials inR3. In such configuration,2kmasses are symmetrically located on thez-axis,2pmasses are symmetrically located on they-axis, and2lmasses are symmetrically located on thex-axis, respectively; the masses symmetrically about the origin are equal.

scholarly journals Central configurations in planar n-body problem with equal masses for $$n=5,6,7$$

2019 ◽  
Vol 131 (10) ◽  
Author(s):  
Małgorzata Moczurad ◽  
Piotr Zgliczyński
Keyword(s):  
Body Problem ◽  
Central Configurations ◽  
Central Configuration ◽  
Newtonian Potential ◽  
Computer Assisted ◽  
Computer Assisted Proof ◽  
N Body Problem ◽  
Reflective Symmetry

Abstract We give a computer-assisted proof of the full listing of central configuration for n-body problem for Newtonian potential on the plane for $$n=5,6,7$$ n = 5 , 6 , 7 with equal masses. We show all these central configurations have a reflective symmetry with respect to some line. For $$n=8,9,10$$ n = 8 , 9 , 10 , we establish the existence of central configurations without any reflectional symmetry.

scholarly journals New Classes of Spatial Central Configurations forN+N+ 2-Body Problem

2012 ◽  
Vol 2012 ◽  
pp. 1-19
Author(s):  
Liu Xuefei ◽  
Zhang Chuntao ◽  
Luo Jianmei ◽  
Zhang Gan
Keyword(s):  
Body Problem ◽  
Central Configurations ◽  
Spatial Central Configurations

scholarly journals Central configurations in the spatial n-body problem for $$n=5,6$$ with equal masses

2020 ◽  
Vol 132 (11-12) ◽  
Author(s):  
Małgorzata Moczurad ◽  
Piotr Zgliczyński
Keyword(s):  
Body Problem ◽  
Central Configurations ◽  
Central Configuration ◽  
Computer Assisted ◽  
Planar Case ◽  
Full List ◽  
Computer Assisted Proof ◽  
N Body Problem

AbstractWe present a computer assisted proof of the full listing of central configurations for spatial n-body problem for $$n=5$$ n = 5 and 6, with equal masses. For each central configuration, we give a full list of its Euclidean symmetries. For all masses sufficiently close to the equal masses case, we give an exact count of configurations in the planar case for $$n=4,5,6,7$$ n = 4 , 5 , 6 , 7 and in the spatial case for $$n=4,5,6$$ n = 4 , 5 , 6 .

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