Periodic orbits of the general three-body problem for the Sun-Jupiter-Saturn system

1985 ◽  
Vol 35 (3) ◽  
pp. 289-303 ◽  
Author(s):  
Johnny H. Kwok ◽  
Paul E. Nacozy
Keyword(s):  
Periodic Orbits ◽  
Body Problem ◽  
The Sun ◽  
Three Body Problem ◽  
Three Body

GLOBAL BEHAVIOR OF THE CHARGED ISOSCELES THREE-BODY PROBLEM

1994 ◽  
Vol 04 (04) ◽  
pp. 865-884 ◽  
Author(s):  
PAU ATELA ◽  
ROBERT I. McLACHLAN
Keyword(s):  
Bifurcation Diagram ◽  
Periodic Orbits ◽  
Body Problem ◽  
Kepler Problem ◽  
Global Bifurcation ◽  
Three Body Problem ◽  
Anisotropic Kepler Problem ◽  
The One ◽  
Three Body ◽  
Limiting Value

We study the global bifurcation diagram of the two-parameter family of ODE’s that govern the charged isosceles three-body problem. (The classic isosceles three-body problem and the anisotropic Kepler problem (two bodies) are included in the same family.) There are two major sources of periodic orbits. On the one hand the “Kepler” orbit, a stable orbit exhibiting the generic bifurcations as the multiplier crosses rational values. This orbit turns out to be the continuation of the classical circular Kepler orbit. On the other extreme we have the collision-ejection orbit which exhibits an “infinite-furcation.” Up to a limiting value of the parameter we have finitely many periodic orbits (for each fixed numerator in the rotation number), passed this value there is a sudden birth of an infinite number of them. We find that these two bifurcations are remarkably connected forming the main “skeleton” of the global bifurcation diagram. We conjecture that this type of global connection must be present in related problems such as the classic isosceles three-body problem and the anisotropic Kepler problem.

New kinds of asymmetric periodic orbits in the restricted three-body problem

1996 ◽  
Vol 240 (2) ◽  
pp. 273-293 ◽  
Author(s):  
C. G. Zagouras ◽  
E. Perdios ◽  
O. Ragos
Keyword(s):  
Periodic Orbits ◽  
Body Problem ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Three Body

scholarly journals Some periodic orbits of general three body problem with vanishing angular momentum

2012 ◽  
pp. 377-389 ◽  
Author(s):  
V. B. Titov ◽  
Keyword(s):  
Angular Momentum ◽  
Periodic Orbits ◽  
Body Problem ◽  
Three Body Problem ◽  
Three Body
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