Periodic orbits and bifurcations in the Sitnikov four-body problem when all primaries are oblate

2013 ◽  
Vol 345 (1) ◽  
pp. 73-83 ◽  
Author(s):  
L. P. Pandey ◽  
I. Ahmad
Keyword(s):  
Periodic Orbits ◽  
Body Problem ◽  
Four Body Problem

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

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 Periodic orbits in the restricted four-body problem with two equal masses

2013 ◽  
Vol 345 (2) ◽  
pp. 247-263 ◽  
Author(s):  
Jaime Burgos-García ◽  
Joaquín Delgado
Keyword(s):  
Periodic Orbits ◽  
Body Problem ◽  
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.

Sign in / Sign up

Export Citation Format

Share Document