Simultaneous binary collisions in the planar four-body problem

Citation
R. Martinez et C. Simo, Simultaneous binary collisions in the planar four-body problem, NONLINEARIT, 12(4), 1999, pp. 903-930
Citations number
20
Categorie Soggetti
Mathematics
Journal title
NONLINEARITY
ISSN journal
09517715 → ACNP
Volume
12
Issue
4
Year of publication
1999
Pages
903 - 930
Database
ISI
SICI code
0951-7715(199907)12:4<903:SBCITP>2.0.ZU;2-R
Abstract
We consider simultaneous binary collisions in the general planar four-body problem. We prove they are regularizable in the sense of continuity with re spect to initial conditions using a blow-up of the singularity. Furthermore , numerical evidence is given that the differentiability of the regularizar ion should be, in general, less than C-8/3. As a Simple example, the double isosceles four-body problem, displays that kind of behaviour.