Rhomboidal And Triangular Four- And Five-body Problems: Planar Central Configurations

2018 ◽  
Author(s):  
Muhammad Shoaib ◽  
Abdul Rehman Kashif ◽  
Iharka Szücs-Csillik
Keyword(s):  
Central Configurations ◽  
Planar Central Configurations

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 Andoyer equations for noncollinear planar central configurations

2017 ◽  
Vol 41 ◽  
pp. 515-523
Author(s):  
Antonio Carlos FERNANDES ◽  
Luis Fernando MELLO
Keyword(s):  
Central Configurations ◽  
Planar Central Configurations

Planar central configuration estimates in the n-body problem

1996 ◽  
Vol 16 (5) ◽  
pp. 1059-1070 ◽  
Author(s):  
Christopher K. McCord
Keyword(s):  
Lower Bound ◽  
Potential Function ◽  
Body Problem ◽  
Morse Function ◽  
Central Configurations ◽  
Central Configuration ◽  
N Body Problem ◽  
Planar Central Configurations

AbstractFor all masses, there are at least n − 2, O2-orbits of non-collinear planar central configurations. In particular, this estimate is valid even if the potential function is not a Morse function. If the potential function is a Morse function, then an improved lower bound, of the order of n! ln(n + 1/3)/2, can be given.

scholarly journals Planar Central Configurations of Symmetric Five-Body Problems with Two Pairs of Equal Masses

2016 ◽  
Vol 2016 ◽  
pp. 1-11 ◽  
Author(s):  
Muhammad Shoaib ◽  
Abdul Rehman Kashif ◽  
Anoop Sivasankaran
Keyword(s):  
Phase Space ◽  
Central Configurations ◽  
Central Configuration ◽  
Isosceles Trapezoid ◽  
Mass Ratios ◽  
Axis Of Symmetry ◽  
Planar Central Configurations

We study central configuration of a set of symmetric planar five-body problems where(1)the five masses are arranged in such a way thatm1,m2, andm4are collinear andm2,m3, andm5are collinear; the two sets of collinear masses form a triangle withm2at the intersection of the two sets of collinear masses;(2)four of the bodies are on the vertices of an isosceles trapezoid and the fifth body can take various positions on the axis of symmetry both outside and inside the trapezoid. We form expressions for mass ratios and identify regions in the phase space where it is possible to choose positive masses which will make the configuration central. We also show that the triangular configuration is not possible.

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