Periodic motion around the triangular equilibrium points of the photogravitational restricted problem of three bodies

1991 ◽  
Vol 51 (4) ◽  
pp. 331-348 ◽  
Author(s):  
C. G. Zagouras
Keyword(s):  
Periodic Motion ◽  
Restricted Problem ◽  
Equilibrium Points

Displacement of the Lagrange Equilibrium Points in the Restricted Three Body Problem With Rigid Body Satellite

1978 ◽  
Vol 41 ◽  
pp. 305-314
Author(s):  
W.J. Robinson
Keyword(s):  
Rigid Body ◽  
Restricted Problem ◽  
Body Problem ◽  
Equilibrium Points ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Three Body

AbstractIn the restricted problem of three point masses, the positions of the equilibrium points are well known and are tabulated. When the satellite is a rigid body, these values no longer correspond to the equilibrium points. This paper seeks to determine the magnitudes of the discrepancies.

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.

scholarly journals Periodic orbits of the second genus near the straight-line equilibrium points in the problem of three bodies

1927 ◽  
Vol 114 (768) ◽  
pp. 490-516
Keyword(s):  
Periodic Orbits ◽  
Restricted Problem ◽  
Equilibrium Points ◽  
Class A ◽  
Straight Line ◽  
Line Equilibrium

It has been shown by Poincaré that periodic orbits of two genera exi in the restricted problem of three bodies. These are designated as the orbi of the First Genus and of the Second Genus. So far as the writer is awai all the periodic orbits which have been constructed up to the present tin with one exception, belong to the first genus. It is the purpose of this pap to construct orbits of the second genus. The particular problem with which we are concerned pertains to the motic of an infinitesimal body in the vicinity of the Lagrangian straight-line equilibriui points. Various memoirs deal with the first genus orbits in the neighbourhood of these points, but we are particularly interested in only one of these, viz., the Oscillating Satellite as determined by Moulton. The second genus orbits with which the present paper deals are in the vicinity of the orbits of Class A of the “Osc. Sat.” Reference must also be made to one of the author’s papers on Asymptotic Satellites, in which are determined the orbits that approach the periodic orbits of Class A asymptotically, as some of the results there obtained are used in the problem now under consideration.

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