The circular restricted 4-body problem with three equal primaries in the collinear central configuration of the 3-body problem

2021 ◽  
Vol 133 (11-12) ◽  
Author(s):  
Jaume Llibre ◽  
Daniel Paşca ◽  
Claudià Valls
Keyword(s):  
Body Problem ◽  
Central Configuration

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 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.

On the uniqueness of the isosceles trapezoidal central configuration in the 4-body problem for power-law potentials

Nonlinearity ◽  
2019 ◽  
Vol 33 (1) ◽  
pp. 388-407
Author(s):  
Antonio Carlos Fernandes ◽  
Luis Fernando Mello ◽  
Claudio Vidal
Keyword(s):  
Power Law ◽  
Body Problem ◽  
Central Configuration

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 .

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.

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