The Family P 12 of the Three-Body Problem — the Simplest Family of Periodic Orbits, with Twelve Symmetries per Period

2001 ◽  
pp. 279-298 ◽  
Author(s):  
C. Marchal
Keyword(s):  
Periodic Orbits ◽  
Body Problem ◽  
Three Body Problem ◽  
The Family ◽  
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.

scholarly journals The family of Quasi-satellite periodic orbits in the circular co-planar RTBP

2014 ◽  
Vol 9 (S310) ◽  
pp. 172-173
Author(s):  
Alexandre Pousse ◽  
Philippe Robutel ◽  
Alain Vienne
Keyword(s):  
Periodic Orbits ◽  
Body Problem ◽  
Real Problem ◽  
Three Body Problem ◽  
The Family ◽  
Circular Case ◽  
Validity Limit ◽  
Stable Family ◽  
Three Body ◽  
Very High

AbstractIn the circular case of the coplanar Restricted Three-body Problem, we studied how the family of quasi-satellite (QS) periodic orbits allows to define an associated libration center. Using the averaged problem, we highlighted a validity limit of this one: for QS orbits with low eccentricities, the averaged problem does not correspond to the real problem. We do the same procedure to L3, L4 and L5 emerging periodic orbits families and remarked that for very high eccentricities ${\cal F}_{L_4}$ and ${\cal F}_{L_5}$ merge with ${\cal F}_{L_3}$ which bifurcates to a stable family.

GLOBAL BEHAVIOR OF THE CHARGED ISOSCELES THREE-BODY PROBLEM

1994 ◽  
Vol 04 (04) ◽  
pp. 865-884 ◽  
Author(s):  
PAU ATELA ◽  
ROBERT I. McLACHLAN
Keyword(s):  
Bifurcation Diagram ◽  
Periodic Orbits ◽  
Body Problem ◽  
Kepler Problem ◽  
Global Bifurcation ◽  
Three Body Problem ◽  
Anisotropic Kepler Problem ◽  
The One ◽  
Three Body ◽  
Limiting Value

We study the global bifurcation diagram of the two-parameter family of ODE’s that govern the charged isosceles three-body problem. (The classic isosceles three-body problem and the anisotropic Kepler problem (two bodies) are included in the same family.) There are two major sources of periodic orbits. On the one hand the “Kepler” orbit, a stable orbit exhibiting the generic bifurcations as the multiplier crosses rational values. This orbit turns out to be the continuation of the classical circular Kepler orbit. On the other extreme we have the collision-ejection orbit which exhibits an “infinite-furcation.” Up to a limiting value of the parameter we have finitely many periodic orbits (for each fixed numerator in the rotation number), passed this value there is a sudden birth of an infinite number of them. We find that these two bifurcations are remarkably connected forming the main “skeleton” of the global bifurcation diagram. We conjecture that this type of global connection must be present in related problems such as the classic isosceles three-body problem and the anisotropic Kepler problem.

scholarly journals LOCATION AND STABILITY OF THE TRIANGULAR POINTS IN THE TRIAXIAL ELLIPTIC RESTRICTED THREE-BODY PROBLEM

2021 ◽  
Vol 57 (2) ◽  
pp. 311-319
Author(s):  
M. Radwan ◽  
Nihad S. Abd El Motelp
Keyword(s):  
Linear Stability ◽  
Periodic Orbits ◽  
Body Problem ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Stability Regions ◽  
Triangular Points ◽  
Problem Frame ◽  
The Stability ◽  
Three Body

The main goal of the present paper is to evaluate the perturbed locations and investigate the linear stability of the triangular points. We studied the problem in the elliptic restricted three body problem frame of work. The problem is generalized in the sense that the two primaries are considered as triaxial bodies. It was found that the locations of these points are affected by the triaxiality coefficients of the primaries and the eccentricity of orbits. Also, the stability regions depend on the involved perturbations. We also studied the periodic orbits in the vicinity of the triangular points.

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