- Turkish Journal of Mathematics
- Vol: 38 Issue: 3
- Central configurations in the collinear 5-body problem
Central configurations in the collinear 5-body problem
Authors : Muhammad Shoaib, Anoop Sivasankaran, Abdulrehman Kashif
Pages : 576-585
Doi:10.3906/mat-1212-3
View : 9 | Download : 6
Publication Date : 9999-12-31
Article Type : Makaleler
Abstract :We study the inverse problem of central configuration of collinear general 4- and 5-body problems. A central configuration for n-body problems is formed if the position vector of each particle with respect to the center of mass is a common scalar multiple of its acceleration. In the 3-body problem, it is always possible to find 3 positive masses for any given 3 collinear positions given that they are central. This is not possible for more than 4-body problems in general. We consider a collinear 5-body problem and identify regions in the phase space where it is possible to choose positive masses that will make the configuration central. In the symmetric case we derive a critical value for the central mass above which no central configurations exist. We also show that in general there is no such restriction on the value of the central mass.Keywords : Central configuration, n-body problem, inverse problem of central configuration