The stability of the triangular points in the elliptic restricted problem

1981 ◽  
Vol 23 (1) ◽  
pp. 89-95 ◽  
Author(s):  
R. Meire
Keyword(s):  
Restricted Problem ◽  
Triangular Points ◽  
Elliptic Restricted Problem ◽  
The Stability

scholarly journals Effect of Perturbed Potentials on the Stability of Libration Points in the Restricted Problem

1979 ◽  
Vol 81 ◽  
pp. 57-57
Author(s):  
K. B. Bhatnagar ◽  
P. P. Hallan
Keyword(s):  
Restricted Problem ◽  
Classical Problem ◽  
Oblate Spheroid ◽  
Libration Points ◽  
The Other ◽  
Triangular Points ◽  
Oblate Spheroids ◽  
The Stability

The location and the stability of the libration points in the restricted problem have been studied when there are perturbations in the potentials between the bodies. It is seen that if the perturbing functions involving the parameters α,α1,α2 satisfy certain conditions, there are five libration points, two triangular and three collinear. It is further observed that the collinear points are unstable and for the triangular points, the range of stability increases or decreases depending upon whether the perturbation point (α,α1,α2) lies on one or the other side of the plane Aα + Bα1 + Cα2 = 0, and it remains the same if the point lies on the plane, where A,B,C depend on the perturbations. The theory is verified in the following four cases: (1) there are no perturbations in the potentials (classical problem), (2) only the bigger primary is an oblate spheroid, (3) both the primaries are oblate spheroids, and (4) the primaries are spherical in shape and the bigger is a source of radiation.

Stability of the triangular points in the elliptic restricted problem of three bodies.

AIAA Journal ◽  
1969 ◽  
Vol 7 (6) ◽  
pp. 1024-1028 ◽  
Author(s):  
K. T. ALFRIEND ◽  
R. H. RAND
Keyword(s):  
Restricted Problem ◽  
Triangular Points ◽  
Elliptic Restricted Problem

scholarly journals A Catalogue of Periodic Orbits in the Elliptic Restricted 3-Body Problem

1992 ◽  
Vol 152 ◽  
pp. 171-174 ◽  
Author(s):  
R. Dvorak ◽  
J. Kribbel
Keyword(s):  
Periodic Orbits ◽  
Restricted Problem ◽  
Body Problem ◽  
Grid Size ◽  
Mass Ratios ◽  
Families Of Periodic Orbits ◽  
Elliptic Restricted Problem ◽  
The Stability

Results of families of periodic orbits in the elliptic restricted problem are shown for some specific resonances. They are calculated for all mass ratios 0 < μ < 1.0 of the primary bodies and for all values of the eccentricity of the orbit of the primaries e < 1.0. The grid size is of 0.01 for both parameters. The classification of the stability is undertaken according to the usual one and the results are compared with the extensive studies by Contopoulos (1986) in different galactical models.

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 .

Stability of the triangular points in the elliptic restricted problem of three bodies

AIAA Journal ◽  
1970 ◽  
Vol 8 (2) ◽  
pp. 221-223 ◽  
Author(s):  
ALI HASAN NAYFEH ◽  
AHMED ALY KAMEL
Keyword(s):  
Restricted Problem ◽  
Triangular Points ◽  
Elliptic Restricted Problem
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