The integrable cases of the planetary three-body problem at first-order resonance

1993 ◽  
Vol 55 (3) ◽  
pp. 249-259 ◽  
Author(s):  
V. N. Shinkin
Keyword(s):  
Body Problem ◽  
Three Body Problem ◽  
Order Resonance ◽  
First Order ◽  
Three Body

scholarly journals A Complete Family of Periodic Solutions of the Planar Three-Body Problem and their Stability

1977 ◽  
Vol 33 ◽  
pp. 159-159
Author(s):  
M. Hénon
Keyword(s):  
Periodic Solutions ◽  
Periodic Orbits ◽  
Body Problem ◽  
The Other ◽  
Three Body Problem ◽  
Complete Family ◽  
First Order ◽  
Hierarchical Arrangement ◽  
The Family ◽  
Three Body

AbstractWe give a complete description of a one-parameter family of periodic orbits in the planar problem of three bodies with equal masses. This family begins with a rectilinear orbit, computed by Schubart in 1956. It ends in retrograde revolution, i.e., a hierarchy of two binaries rotating in opposite directions. The first-order stability of the orbits in the plane is also computed. Orbits of the retrograde revolution type are stable; more unexpectedly, orbits of the “interplay” type at the other end of the family are also stable. This indicates the possible existence of triple stars with a motion entirely different from the usual hierarchical arrangement.

Networks of periodic orbits in the circular restricted three-body problem with first order post-Newtonian terms

Meccanica ◽  
2019 ◽  
Vol 54 (15) ◽  
pp. 2339-2365 ◽  
Author(s):  
Euaggelos E. Zotos ◽  
K. E. Papadakis ◽  
Md Sanam Suraj ◽  
Amit Mittal ◽  
Rajiv Aggarwal
Keyword(s):  
Periodic Orbits ◽  
Body Problem ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
First Order ◽  
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 Study of the stability of the perturbed solutions of the restricted three body problem

BIBECHANA ◽  
2015 ◽  
Vol 13 ◽  
pp. 18-22
Author(s):  
MAA Khan ◽  
MR Hassan ◽  
RR Thapa
Keyword(s):  
Body Problem ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Variational Equations ◽  
First Order ◽  
Characteristic Exponents ◽  
Method Of Determination ◽  
The Stability ◽  
Three Body

In this paper we have been examined the stability of the perturbed solutions of the restricted three body problem. We have been restricted ourselves only to the first order variational equations. Our variational equations depend on the periodic solutions. Here the applications of the method of Fuchs and Floquet Proves to be complicated and hence we have been preferred Poincare's Method of determination of the characteristic exponents. With the determination of the characteristic exponents we have been abled to conclude regarding the stability of the generating solution. We have obtained that the motions are unstable in all the cases. By Poincare's implicit function theorem we have concluded that the stability would remain the same for small value of the parameter m and in all types of motion of the restricted three-body problem.BIBECHANA 13 (2016) 18-22 

Three-body problem and elliptic integrals

1966 ◽  
Vol 25 ◽  
pp. 194-196
Author(s):  
F. Schmeidler
Keyword(s):  
Body Problem ◽  
Elliptic Integrals ◽  
Three Body Problem ◽  
First Order ◽  
Three Body

In an earlier paper (1) it was shown that there are certain cases in the three-body problem in which all perturbations of the first order can be represented by elliptic integrals. Some more cases of such sort are outlined here.

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