PERIODIC SOLUTIONS NEAR THE LAGRANGE EQUILIBRIUM POINTS IN THE RESTRICTED THREE-BODY PROBLEM, FOR MASS RATIOS NEAR ROUTH'S CRITICAL VALUE

1991 ◽  
pp. 3-32
Author(s):  
Gianfausto DELL'ANTONIO
Keyword(s):  
Periodic Solutions ◽  
Body Problem ◽  
Equilibrium Points ◽  
Critical Value ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Mass Ratios ◽  
Three Body

Resonant Three-Dimensional Periodic Solutions About the Triangular Equilibrium Points in the Restricted Problem

1983 ◽  
Vol 74 ◽  
pp. 235-247 ◽  
Author(s):  
C.G. Zagouras ◽  
V.V. Markellos
Keyword(s):  
Periodic Solutions ◽  
Restricted Problem ◽  
Body Problem ◽  
Equilibrium Points ◽  
Mass Parameter ◽  
Three Dimensional ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Special Values ◽  
Three Body

AbstractIn the three-dimensional restricted three-body problem, the existence of resonant periodic solutions about L4 is shown and expansions for them are constructed for special values of the mass parameter, by means of a perturbation method. These solutions form a second family of periodic orbits bifurcating from the triangular equilibrium point. This bifurcation is the evolution, as μ varies continuously, of a regular vertical bifurcation point on the corresponding family of planar periodic solutions emanating from L4.

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