scholarly journals Existence and linear stability of the rhomboidal periodic orbit in the planar equal mass four-body problem

2012 ◽  
Vol 388 (2) ◽  
pp. 942-951 ◽  
Author(s):  
Duokui Yan
Keyword(s):  
Periodic Orbit ◽  
Linear Stability ◽  
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.

Exploring the Location and Linear Stability of the Equilibrium Points in the Equilateral Restricted Four-Body Problem

2020 ◽  
Vol 30 (10) ◽  
pp. 2050155
Author(s):  
Euaggelos E. Zotos
Keyword(s):  
Linear Stability ◽  
Body Problem ◽  
Equilibrium Points ◽  
Libration Points ◽  
The Other ◽  
Classification Method ◽  
Four Body Problem ◽  
The Masses ◽  
Stable Points ◽  
Planar Version

The planar version of the equilateral restricted four-body problem, with three unequal masses, is numerically investigated. By adopting the grid classification method we locate the coordinates, on the plane [Formula: see text], of the points of equilibrium, for all possible values of the masses of the primaries. The linear stability of the libration points is also determined, as a function of the masses. Our analysis indicates that linearly stable points of equilibrium exist only when one of the primaries has a considerably larger mass, with respect to the other two primary bodies, when the triangular configuration of the primaries is also dynamically stable.

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.

scholarly journals Linear stability of double–double orbits in the parallelogram four-body problem

2016 ◽  
Vol 433 (2) ◽  
pp. 785-802 ◽  
Author(s):  
Hao Peng ◽  
Duokui Yan ◽  
Shijie Xu ◽  
Tiancheng Ouyang
Keyword(s):  
Linear Stability ◽  
Body Problem ◽  
Four Body Problem

scholarly journals Linear stability for some symmetric periodic simultaneous binary collision orbits in the four-body problem

2010 ◽  
Vol 108 (2) ◽  
pp. 147-164 ◽  
Author(s):  
Lennard F. Bakker ◽  
Tiancheng Ouyang ◽  
Duokui Yan ◽  
Skyler Simmons ◽  
Gareth E. Roberts
Keyword(s):  
Linear Stability ◽  
Body Problem ◽  
Binary Collision ◽  
Four Body Problem ◽  
Collision Orbits
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