Analytical and numerical construction of vertical periodic orbits about triangular libration points based on polynomial expansion relations among directions

2017 ◽  
Vol 362 (8) ◽  
Author(s):  
Ying-Jing Qian ◽  
Xiao-Dong Yang ◽  
Guan-Qiao Zhai ◽  
Wei Zhang
Keyword(s):  
Periodic Orbits ◽  
Libration Points ◽  
Polynomial Expansion ◽  
Numerical Construction ◽  
Triangular Libration Points

scholarly journals Periodic orbits around the collinear libration points

2016 ◽  
Vol 09 (04) ◽  
pp. 1716-1727 ◽  
Author(s):  
E.I. Abouelmagd ◽  
F. Alzahrani ◽  
A. Hobiny ◽  
J. L. G. Guirao ◽  
M. Alhothuali
Keyword(s):  
Periodic Orbits ◽  
Libration Points

PERIODIC AND ASYMPTOTIC ORBITS IN A FIVE BODY PROBLEM

1944 ◽  
Vol 22a (1) ◽  
pp. 1-25
Author(s):  
Daniel Buchanan
Keyword(s):  
Angular Velocity ◽  
Periodic Orbits ◽  
Body Problem ◽  
Two Dimensions ◽  
Libration Points ◽  
Three Dimensions ◽  
Centre Of Gravity ◽  
Asymptotic Orbits ◽  
Body Subject

Periodic and asymptotic orbits are obtained for the motion of an infinitesimal body subject to the Newtonian attraction of four finite bodies. The finite bodies are equal in mass and remain relatively fixed at the vertices of a square while they revolve about their common centre of gravity with uniform angular velocity. The infinitesimal body moves in the vicinity of the 13 libration points of the finite bodies. Asymptotic orbits of two dimensions and periodic orbits of two and of three dimensions are obtained.

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