A search for collision orbits in the free-fall three-body problem I. Numerical procedure

1995 ◽  
Vol 62 (4) ◽  
pp. 335-362 ◽  
Author(s):  
Kiyotaka Tanikawa ◽  
Hiroaki Umehara ◽  
Hiroshi Abe
Keyword(s):  
Body Problem ◽  
Numerical Procedure ◽  
Free Fall ◽  
Three Body Problem ◽  
Three Body ◽  
Collision Orbits

Periodic orbits in the free-fall three-body problem

2016 ◽  
Vol 60 (12) ◽  
pp. 1083-1089 ◽  
Author(s):  
V. V. Orlov ◽  
V. A. Titov ◽  
L. A. Shombina
Keyword(s):  
Periodic Orbits ◽  
Body Problem ◽  
Free Fall ◽  
Three Body Problem ◽  
Three Body

scholarly journals A note on the existence of invariant punctured tori in the planar circular restricted three-body problem

1988 ◽  
Vol 8 (8) ◽  
pp. 63-72 ◽  
Keyword(s):  
Body Problem ◽  
Small Mass ◽  
Connected Components ◽  
Restricted Three Body Problem ◽  
Three Body Problem ◽  
Jacobi Constant ◽  
Hill Region ◽  
The Masses ◽  
Three Body ◽  
Collision Orbits

AbstractThe existence of transversal ejection—collision orbits in the restricted three-body problem is shown to imply, via the KAM theorem, the existence, for certain intervals of (large) values of the Jacobi constant, of an uncountable number of invariant punctured tori in the corresponding (non-compact) energy surface. The proof is based on a comparison between Levi-Civita and McGehee regularizing variables. That these transversal ejection-collision orbits do actually exist was proved in [5] in the case where one of the primaries has a small mass and the zero-mass body revolves around the other (and for all values of the Jacobi constant compatible with the existence of three connected components for the Hill region); it is proved here without any restriction on the masses, well in the spirit of Conley's thesis [3].

scholarly journals Symbolic Dynamics, Mixing and Entropy in the Three-Body Problem

2016 ◽  
Vol 25 (3) ◽  
Author(s):  
A. Mylläri ◽  
V. Orlov ◽  
A. Chernin ◽  
A. Martynova ◽  
T. Mylläri
Keyword(s):  
Symbolic Dynamics ◽  
Body Problem ◽  
Initial Conditions ◽  
Free Fall ◽  
Equal Mass ◽  
Binary Collision ◽  
Three Body Problem ◽  
Symbolic Sequences ◽  
Three Body ◽  
Sensitivity To Initial Conditions

AbstractWe use symbolic dynamics in the classic equal-mass free-fall three-body problem. Different methods for constructing symbolic sequences (in the process of numerical integration of trajectories) allow one to demonstrate (and illustrate on the Agekian-Anosova map) sensitivity to initial conditions, estimate entropies (Shannon, Markov and others), plot binary collision curves, reveal systems with intensive triple interactions (interplay), etc.

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