scholarly journals Asymptotic Density of Collision Orbits in the Restricted Circular Planar 3 Body Problem

2019 ◽  
Vol 233 (2) ◽  
pp. 799-836 ◽  
Author(s):  
Marcel Guardia ◽  
Vadim Kaloshin ◽  
Jianlu Zhang
Keyword(s):  
Body Problem ◽  
Asymptotic Density ◽  
Collision Orbits

scholarly journals Ejection-Collision orbits in the symmetric collinear four–body problem

2019 ◽  
Vol 71 ◽  
pp. 82-100 ◽  
Author(s):  
M. Alvarez-Ramírez ◽  
E. Barrabés ◽  
M. Medina ◽  
M. Ollé
Keyword(s):  
Body Problem ◽  
Four Body Problem ◽  
Collision Orbits

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].

Global Regularization of a Restricted Four-Body Problem

2014 ◽  
Vol 24 (07) ◽  
pp. 1450092 ◽  
Author(s):  
Martha Alvarez-Ramírez ◽  
Joaquín Delgado ◽  
Claudio Vidal
Keyword(s):  
Numerical Integration ◽  
Body Problem ◽  
Binary Collision ◽  
Type Transformation ◽  
Collision Singularity ◽  
Double Collision ◽  
N Body Problem ◽  
Four Body Problem ◽  
Collision Orbits ◽  
Global Regularization

In the n-body problem, a collision singularity occurs when the position of two or more bodies coincide. By understanding the dynamics of collision motion in the regularized setting, a better understanding of the dynamics of near-collision motion is achieved. In this paper, we show that any double collision of the planar equilateral restricted four-body problem can be regularized by using a Birkhoff-type transformation. This transformation has the important property to provide a simultaneous regularization of three singularities due to binary collision. We present some ejection–collision orbits after the regularization of the restricted four-body problem (RFBP) with equal masses, which were obtained by numerical integration.

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