scholarly journals Classification of periodic orbits in the planar equal-mass four-body problem

2015 ◽  
Author(s):  
Zhifu Xie ◽  
Tiancheng Ouyang ◽  
Duokui Yan
Keyword(s):  
Periodic Orbits ◽  
Body Problem ◽  
Equal Mass ◽  
Four Body Problem

Multiple Periodic Orbits Connecting a Collinear Configuration and a Double Isosceles Configuration in the Planar Equal-Mass Four-Body Problem

2017 ◽  
Vol 17 (4) ◽  
pp. 819-835 ◽  
Author(s):  
Bixiao Shi ◽  
Rongchang Liu ◽  
Duokui Yan ◽  
Tiancheng Ouyang
Keyword(s):  
Periodic Orbit ◽  
Variational Method ◽  
Periodic Orbits ◽  
Body Problem ◽  
Equal Mass ◽  
Local Action ◽  
Collision Singularity ◽  
Four Body Problem ◽  
Multiple Periodic Orbits ◽  
The One

AbstractBy applying our variational method, we show that there exist 24 local action minimizers connecting two prescribed configurations: a collinear configuration and a double isosceles configuration in {H^{1}([0,1],\chi)} in the planar equal-mass four-body problem. Among the 24 local action minimizers, we prove that the one with the smallest action has no collision singularity and it can be extended to a periodic or quasi-periodic orbit. Furthermore, if all the 24 local action minimizers are free of collision, we show that they can generate sixteen different periodic orbits.

Periodic orbits in the restricted four-body problem

1986 ◽  
Vol 13 (8) ◽  
pp. 473-479 ◽  
Author(s):  
K.C. Howell ◽  
D.B. Spencer
Keyword(s):  
Periodic Orbits ◽  
Body Problem ◽  
Four Body Problem

scholarly journals New periodic orbits in the planar equal-mass three-body problem

2018 ◽  
Vol 38 (4) ◽  
pp. 2187-2206
Author(s):  
Rongchang Liu ◽  
◽  
Jiangyuan Li ◽  
Duokui Yan
Keyword(s):  
Periodic Orbits ◽  
Body Problem ◽  
Equal Mass ◽  
Three Body Problem ◽  
Three Body

The Existence of Retrograde Orbits for the Four-Body Problem with Various Choices of Masses

2013 ◽  
Vol 871 ◽  
pp. 101-106
Author(s):  
Chong Li
Keyword(s):  
Variational Methods ◽  
Periodic Orbits ◽  
Opposite Direction ◽  
Body Problem ◽  
Topological Type ◽  
The Other ◽  
Action Functional ◽  
Four Body Problem

In this paper, we study the planar Newtonian four-body problem with various choices of masses. We prove that there exist infinitely many periodic and quasi-periodic orbits with certain topological type, called retrograde orbits, that minimize the action functional on certain path spaces. On these orbits, two particles revolve around each other in one direction, while the other two particles travel on themselves orbits in opposite direction, respectively. Our proof is based on variational methods inspired by the work of Kuo-Chang Chen.

Periodic orbits and bifurcations in the Sitnikov four-body problem

2008 ◽  
Vol 100 (4) ◽  
pp. 251-266 ◽  
Author(s):  
P. S. Soulis ◽  
K. E. Papadakis ◽  
T. Bountis
Keyword(s):  
Periodic Orbits ◽  
Body Problem ◽  
Four Body Problem

scholarly journals The Axisymmetric Central Configurations of the Four-Body Problem with Three Equal Masses

Symmetry ◽  
2020 ◽  
Vol 12 (4) ◽  
pp. 648
Author(s):  
Emese Kővári ◽  
Bálint Érdi
Keyword(s):  
Analytical Solution ◽  
Body Problem ◽  
Equal Mass ◽  
The Other ◽  
Coordinate Space ◽  
Four Body Problem ◽  
Axis Of Symmetry ◽  
The Masses ◽  
Special Case ◽  
Two Bodies

In the studied axisymmetric case of the central four-body problem, the axis of symmetry is defined by two unequal-mass bodies, while the other two bodies are situated symmetrically with respect to this axis and have equal masses. Here, we consider a special case of the problem and assume that three of the masses are equal. Using a recently found analytical solution of the general case, we formulate the equations of condition for three equal masses analytically and solve them numerically. A complete description of the problem is given by providing both the coordinates and masses of the bodies. We show furthermore how the three-equal-mass solutions are related to the general case in the coordinate space. The physical aspects of the configurations are also studied and discussed.

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