Periodic Solution of the Three-Dimensional Restricted Three Body Problem Representing Analytic Continuation of Keplerian Rectilinear Periodic Motion

1986 ◽  
pp. 17-25
Author(s):  
A. Ahmad ◽  
M. N. Huda
Keyword(s):  
Periodic Solution ◽  
Analytic Continuation ◽  
Periodic Motion ◽  
Body Problem ◽  
Three Dimensional ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Three Body

scholarly journals Periodic Solution of the restricted three body problem

BIBECHANA ◽  
2013 ◽  
Vol 10 ◽  
pp. 44-51
Author(s):  
MR Hassan ◽  
RR Thapa
Keyword(s):  
Periodic Solution ◽  
Analytic Continuation ◽  
Centrifugal Force ◽  
Periodic Motion ◽  
Body Problem ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
First Order ◽  
Three Body

The effect of perturbation in centrifugal force on the periodic solution of the restricted three-body problem representing analytic continuation of Keplerian rectilinear periodic motion has been examined. However, we have taken the perturbation in the centrifugal force to be of the order of μ, the reduced mass of the smaller primary. We have calculated the first order perturbations also. BIBECHANA 10 (2014) 44-51 DOI: http://dx.doi.org/10.3126/bibechana.v10i0.9310

scholarly journals Regular and Chaotic Motion in a Restricted Three–Body Problem of Astrophysical Interest

2000 ◽  
Vol 174 ◽  
pp. 281-285 ◽  
Author(s):  
J. C. Muzzio ◽  
F. C. Wachlin ◽  
D. D. Carpintero
Keyword(s):  
External Field ◽  
Body Problem ◽  
Stellar System ◽  
Three Dimensional ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Stellar Orbits ◽  
System A ◽  
Regular And Chaotic Motion ◽  
Three Body

AbstractWe have studied the motion of massless particles (stars) bound to a stellar system (a galactic satellite) that moves on a circular orbit in an external field (a galaxy). A large percentage of the stellar orbits turned out to be chaotic, contrary to what happens in the usual restricted three–body problem of celestial mechanics where most of the orbits are regular. The discrepancy is probably due to three facts: 1) Our study is not limited to orbits on the main planes of symmetry, but considers three–dimensional motion; 2) The force exerted by the satellite goes to zero (rather than to infinity) at the center of the satellite; 3) The potential of the satellite is triaxial, rather than spherical.

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.

Periodic solution of the nonlinear Sitnikov restricted three-body problem

New Astronomy ◽  
2020 ◽  
Vol 75 ◽  
pp. 101319 ◽  
Author(s):  
Elbaz I. Abouelmagd ◽  
Juan Luis García Guirao ◽  
Ashok Kumar Pal
Keyword(s):  
Periodic Solution ◽  
Body Problem ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Three Body

scholarly journals Three Dimensional Stability of A Rectilinear Periodic Solution of the Three-Body Problem, for all Values of the Masses

1977 ◽  
Vol 33 ◽  
pp. 161-161
Author(s):  
M. Hénon
Keyword(s):  
Periodic Solution ◽  
Dimensional Stability ◽  
Body Problem ◽  
Central Body ◽  
Three Dimensional ◽  
Three Body Problem ◽  
Stability And Instability ◽  
The Masses ◽  
Three Body ◽  
Triple Stars

AbstractWe consider a rectilinear periodic solution in which the central body collides alternately with each of the two other bodies. This solution is found to exist for all values of the three masses. Its stability with respect to three-dimensional perturbations is computed. Domains of stability and instability are delimited in a triangular mass diagram. Large domains of stability are found. This reinforces the conclusion that triple stars may have an “interplay” type of motion.

BIFURCATIONS IN THE TOPOLOGY OF ZERO-VELOCITY SURFACES IN THE PHOTO-GRAVITATIONAL COPENHAGEN PROBLEM

2009 ◽  
Vol 19 (03) ◽  
pp. 1097-1111 ◽  
Author(s):  
T. J. KALVOURIDIS
Keyword(s):  
Body Problem ◽  
Small Body ◽  
Three Dimensional ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Zero Velocity ◽  
Radiation Sources ◽  
Trapping Regions ◽  
Zero Velocity Surfaces ◽  
Three Body

We study the evolution of the regions where three-dimensional motions of a small body are allowed in the Copenhagen case of the restricted three-body problem where one or both primaries, are radiation sources. We discuss the bifurcations in the topology of the zero-velocity surfaces, as well as in the trapping regions of the particle motion for various cases.

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