scholarly journals New Results for the Linear Stability of the Triangular Points in the Elliptic Restricted Problem

1983 ◽  
Vol 74 ◽  
pp. 289-299
Author(s):  
R. Meire
Keyword(s):  
Periodic Solutions ◽  
Linear Stability ◽  
Restricted Problem ◽  
Triangular Points ◽  
Elliptic Restricted Problem ◽  
The Hill ◽  
Transition Curves

AbstractNew results are obtained for the linear stability of the triangular points in the elliptic restricted problem using the Hill equations which describe the infinitesimal motion around L4,L5. Also the shape of the 4Π-periodic solutions along the transition curves in the μ-e plane is investigated .

Periodic Trojan orbits in the elliptic restricted problem

1966 ◽  
Vol 25 ◽  
pp. 176-186
Author(s):  
E. Rabe
Keyword(s):  
Periodic Solution ◽  
Periodic Solutions ◽  
Restricted Problem ◽  
Angular Motion ◽  
Basic Period ◽  
Short Period ◽  
Elliptic Restricted Problem ◽  
The Mean

As previously shown the generally non-periodic librations about the equilateral points of the plane elliptic restricted problem depend on three frequencies. After elimination of the short-period oscillations, the solutions depend on the libration frequencynand the mean angular motionNof Jupiter. Whenn/Nis commensurable the librations become periodic. One periodic solution corresponds to the actual Trojans, but additional planar solutions exist also with periods equal to multiples of the basic period. For some specific values of the eccentricityethese solutions are accompanied by an associated sequence of non-planar periodic solutions. The values ofedepend slightly on the inclinationi.

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