Blow up of Total Collision in the Tetrahedral Non-Rotating Four Body Problem

2004 ◽  
pp. 77-94 ◽  
Author(s):  
Joaquín Delgado ◽  
Claudio Vidal
Keyword(s):  
Body Problem ◽  
Blow Up ◽  
Four Body Problem ◽  
Total Collision

scholarly journals Central Configurations and Action Minimizing Orbits in Kite Four-Body Problem

2020 ◽  
Vol 2020 ◽  
pp. 1-18
Author(s):  
B. Benhammouda ◽  
A. Mansur ◽  
M. Shoaib ◽  
I. Szücs-Csillik ◽  
D. Offin
Keyword(s):  
Cross Sections ◽  
Body Problem ◽  
Mass Parameter ◽  
Central Configurations ◽  
Continuous Family ◽  
Classical Action ◽  
Dynamical Aspect ◽  
Homographic Solutions ◽  
Four Body Problem ◽  
Current Article

In the current article, we study the kite four-body problems with the goal of identifying global regions in the mass parameter space which admits a corresponding central configuration of the four masses. We consider two different types of symmetrical configurations. In each of the two cases, the existence of a continuous family of central configurations for positive masses is shown. We address the dynamical aspect of periodic solutions in the settings considered and show that the minimizers of the classical action functional restricted to the homographic solutions are the Keplerian elliptical solutions. Finally, we provide numerical explorations via Poincaré cross-sections, to show the existence of periodic and quasiperiodic solutions within the broader dynamical context of the four-body problem.

11Li-12C scattering as a four-body problem

1995 ◽  
Vol 21 (1) ◽  
pp. 87-100 ◽  
Author(s):  
J Formanek ◽  
R J Lombard
Keyword(s):  
Body Problem ◽  
Four Body Problem

scholarly journals Symmetries in central-force problems

2003 ◽  
pp. 47-52 ◽  
Author(s):  
V. Mioc ◽  
M. Barbosu
Keyword(s):  
Vector Fields ◽  
Body Problem ◽  
Blow Up ◽  
Central Force ◽  
Polar Coordinates ◽  
Global Flow ◽  
Two Body Problem ◽  
Concrete Problem ◽  
Central Force Problems ◽  
Force Problem

The two-body problem in central fields (reducible to a central-force problem) models a lot of concrete astronomical situations. The corresponding vector fields (in Cartesian and polar coordinates, extended via collision-blow-up and infinity-blow-up transformations) exhibit nice symmetries that form eight-element Abelian groups endowed with an idempotent structure. All these groups are isomorphic, which is not a trivial result, given the different structures of the corresponding phase spaces. Each of these groups contains seven four-element subgroups isomorphic to Klein?s group. These symmetries are of much help in understanding various characteristics of the global flow of the general problem or of a concrete problem at hand, and are essential in searching for periodic orbits.

scholarly journals Dynamics of the the dihedral four-body problem

2012 ◽  
Vol 6 (4) ◽  
pp. 925-974
Author(s):  
Davide L. Ferrario ◽  
Alessandro Portaluri
Keyword(s):  
Body Problem ◽  
Four Body Problem

A restricted charged four-body problem

1990 ◽  
Vol 47 (3) ◽  
pp. 245-266 ◽  
Author(s):  
J. Casasayas ◽  
A. Nunes
Keyword(s):  
Body Problem ◽  
Four Body Problem
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