The flow of the N-body problem near a simultaneous-binary-collision singularity and integrals of motion on the collision manifold

1996 ◽  
Vol 134 (4) ◽  
pp. 303-340 ◽  
Author(s):  
Mohamed Sami ElBialy
Keyword(s):  
Body Problem ◽  
Binary Collision ◽  
Integrals Of Motion ◽  
Collision Singularity ◽  
N Body Problem ◽  
Collision Manifold

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.

scholarly journals Collision dynamics in Hénon-Heiles’ two-body problem

2003 ◽  
pp. 43-46 ◽  
Author(s):  
V. Mioc ◽  
M. Barbosu
Keyword(s):  
Body Problem ◽  
Blow Up ◽  
Collision Dynamics ◽  
Two Body Problem ◽  
Collision Singularity ◽  
Collision Manifold ◽  
Special Case

We tackle the two-body problem associated to H?non-Heiles? potential in the special case of the collision singularity. Using McGehee-type transformations of the second kind, we blow up the singularity and replace it by the collision manifold Mc pasted on the phase spece. We fully describe the flow on Mc. This flow is similar to analogous flows met in post-Newtonian two-body problems.

The binary collision in the N-body problem

Icarus ◽  
1968 ◽  
Vol 9 (1-3) ◽  
pp. 305-314 ◽  
Author(s):  
Hans J. Sperling
Keyword(s):  
Body Problem ◽  
Binary Collision ◽  
N Body Problem

scholarly journals On frequency estimations in phase fitted variational integrators for the general N-body problem

PAMM ◽  
2013 ◽  
Vol 13 (1) ◽  
pp. 33-34
Author(s):  
Odysseas Kosmas ◽  
Sigrid Leyendecker
Keyword(s):  
Body Problem ◽  
Variational Integrators ◽  
N Body Problem
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