The collision singularity in a perturbedN-body problem

1972 ◽  
Vol 5 (3) ◽  
pp. 396-406 ◽  
Author(s):  
Hans J. Sperling
Keyword(s):  
Body Problem ◽  
Collision Singularity

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.

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.

Multiple Periodic Orbits Connecting a Collinear Configuration and a Double Isosceles Configuration in the Planar Equal-Mass Four-Body Problem

2017 ◽  
Vol 17 (4) ◽  
pp. 819-835 ◽  
Author(s):  
Bixiao Shi ◽  
Rongchang Liu ◽  
Duokui Yan ◽  
Tiancheng Ouyang
Keyword(s):  
Periodic Orbit ◽  
Variational Method ◽  
Periodic Orbits ◽  
Body Problem ◽  
Equal Mass ◽  
Local Action ◽  
Collision Singularity ◽  
Four Body Problem ◽  
Multiple Periodic Orbits ◽  
The One

AbstractBy applying our variational method, we show that there exist 24 local action minimizers connecting two prescribed configurations: a collinear configuration and a double isosceles configuration in {H^{1}([0,1],\chi)} in the planar equal-mass four-body problem. Among the 24 local action minimizers, we prove that the one with the smallest action has no collision singularity and it can be extended to a periodic or quasi-periodic orbit. Furthermore, if all the 24 local action minimizers are free of collision, we show that they can generate sixteen different periodic orbits.

The Mind-Body Problem Revisited

1975 ◽  
Vol 20 (8) ◽  
pp. 660-660
Author(s):  
MADGE SCHEIBEL ◽  
ARNOLD SCHEIBEL
Keyword(s):  
Body Problem ◽  
Mind Body Problem ◽  
The Mind

The Nuclear Many-Body Problem

1980 ◽  
Author(s):  
Peter Ring ◽  
Peter Schuck
Keyword(s):  
Body Problem ◽  
Many Body

Zombies and Dolls

2018 ◽  
Author(s):  
Marcello Massimini ◽  
Giulio Tononi
Keyword(s):  
Body Problem ◽  
Thought Experiments ◽  
Turing Test ◽  
Hard Problem ◽  
Mind Body Problem ◽  
The Hard Problem ◽  
The Mind ◽  
The Brain

This chapter uses thought experiments and practical examples to introduce, in a very accessible way, the hard problem of consciousness. Soon, machines may behave like us to pass the Turing test and scientists may succeed in copying and simulating the inner workings of the brain. Will all this take us any closer to solving the mysteries of consciousness? The reader is taken to meet different kind of zombies, the philosophical, the digital, and the inner ones, to understand why many, scientists and philosophers alike, doubt that the mind–body problem will ever be solved.

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