Pair Collision Transition Operators of the Three-Body Problem on a Line

1997 ◽  
Vol 12 (01) ◽  
pp. 119-124
Author(s):  
P.G. Akishin ◽  
I.V. Puzynin ◽  
S.I. Vinitsky
Keyword(s):  
Computer Simulations ◽  
Taylor Series ◽  
Body Problem ◽  
Numerical Study ◽  
Dynamical Problem ◽  
Three Body Problem ◽  
First Results ◽  
Free Parameters ◽  
Three Body ◽  
Transition Operators

The system of three gravitating particles on a line is considered. The forward and backward expansions of the solution in the Taylor series are used for numerical study of the problem. On the basis of the description of the solutions in the vicinity of pair collision points the pair collision transition operators are introduced. The dynamical problem is reduced to the study of the 2D-maps in the space of free parameters of the system in the vicinity of pair collision points. The first results of the computer simulations are presented.

scholarly journals Numerical Investigation for Periodic Orbits in the Hill Three-Body Problem

Universe ◽  
2020 ◽  
Vol 6 (6) ◽  
pp. 72 ◽  
Author(s):  
Vassilis S. Kalantonis
Keyword(s):  
Periodic Orbits ◽  
Body Problem ◽  
Numerical Study ◽  
Three Dimensional ◽  
Earth Satellite ◽  
Mission Design ◽  
Special Importance ◽  
Three Body Problem ◽  
Three Body ◽  
The Hill

The current work performs a numerical study on periodic motions of the Hill three-body problem. In particular, by computing the stability of its basic planar families we determine vertical self-resonant (VSR) periodic orbits at which families of three-dimensional periodic orbits bifurcate. It is found that each VSR orbit generates two such families where the multiplicity and symmetry of their member orbits depend on certain property characteristics of the corresponding VSR orbit’s stability. We trace twenty four bifurcated families which are computed and continued up to their natural termination forming thus a manifold of three-dimensional solutions. These solutions are of special importance in the Sun-Earth-Satellite system since they may serve as reference orbits for observations or space mission design.

scholarly journals On the dynamics of Trojan planets in extrasolar planetary systems

2007 ◽  
Vol 3 (S249) ◽  
pp. 461-468 ◽  
Author(s):  
R. Dvorak ◽  
R. Schwarz ◽  
Ch. Lhotka
Keyword(s):  
Body Problem ◽  
Equilibrium Points ◽  
Planetary Systems ◽  
Outer Planet ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Eccentric Orbit ◽  
Numerical Integrations ◽  
First Results ◽  
Three Body

AbstractIn this article we examine the motion of fictitious Trojan planets close to the equilateral Lagrangean equilibrium points in extrasolar planetary systems. Whether there exist stable motion in this area or not depends on the massratio of the primariy bodies in the restricted three body problem, namely the host star and the gasgiant. Taking into account also the eccentricity of the primaries we show via results of extensive numerical integrations that Trojan planets may survive only for e < 0.25. We also show first results of a mapping in the 1:1 resonance with a gas giant on an eccentric orbit which is applied to the extrasolar planetary systems HD 17051. We furthermore study the influence of an additional outer planet which perturbs the motion of the gasgiant as well as the Trojan cloud around its L4 Lagrangean point.

Rigid-Rotator and Fixed-Shape Solutions to the Coulomb Three-Body Problem

1997 ◽  
Vol 22 (1) ◽  
pp. 37-60 ◽  
Author(s):  
A. Santander ◽  
J. Mahecha ◽  
F. Pérez
Keyword(s):  
Body Problem ◽  
Three Body Problem ◽  
Rigid Rotator ◽  
Three Body
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