An invariant relation in the elliptic restricted problem of three bodies. II - Trojan asteroids

1978 ◽  
Vol 83 ◽  
pp. 664
Author(s):  
Z. Vrcelj ◽  
J. H. Kiewiet de Jonge
Keyword(s):  
Restricted Problem ◽  
Invariant Relation ◽  
Trojan Asteroids ◽  
Elliptic Restricted Problem

scholarly journals Orbital Stability in the Elliptic Restricted Three Body Problem

1978 ◽  
Vol 41 ◽  
pp. 333-337
Author(s):  
C.A. Williams ◽  
J.G. Watts
Keyword(s):  
Restricted Problem ◽  
Body Problem ◽  
Orbital Stability ◽  
Restricted Three Body Problem ◽  
Invariant Relation ◽  
Three Body Problem ◽  
Hill Stability ◽  
Elliptic Restricted Problem ◽  
Three Body

AbstractBased on the concept of orbital stability introduced by G. W. Hill, a method is presented to facilitate the determination of the orbital stability of solutions to the planar elliptic restricted problem of three bodies. The invariant relation introduced by Szebehely and Giacaglia (1964) contains an integral which is expanded here about a Keplerian solution to the problem. If the expansion converges, it can be used to determine the conditions for Hill stability. With it one can also define stability in a periodic sense.

scholarly journals The Mechanism of Branching of Three-Dimensional Periodic Orbits from the Plane

1983 ◽  
Vol 74 ◽  
pp. 213-224
Author(s):  
I.A. Robin ◽  
V.V. Markellos
Keyword(s):  
Recent Work ◽  
Periodic Orbits ◽  
Restricted Problem ◽  
Three Dimensional ◽  
General Situation ◽  
Orbital Symmetry ◽  
Resonant Orbits ◽  
Symmetry Properties ◽  
Elliptic Restricted Problem ◽  
Symmetric Periodic Orbits

AbstractA linearised treatment is presented of vertical bifurcations of symmetric periodic orbits(bifurcations of plane with three-dimensional orbits) in the circular restricted problem. Recent work on bifurcations from vertical-critical orbits (av = ±1) is extended to deal with the v more general situation of bifurcations from vertical self-resonant orbits (av = cos(2Πn/m) for integer m,n) and it is shown that in this more general case bifurcating families of three-dimensional orbits always occur in pairs, the orbital symmetry properties being governed by the evenness or oddness of the integer m. The applicability of the theory to the elliptic restricted problem is discussed.

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