Colloquium/CSUMS Lecture

Starts: November 6, 2009 at 3:00 PM
Location: Jones Hall 301
Contact: Junping Shi

Summary

Speaker: Zhifu Xie (Virginia State University)

Full Description

Title: Central Configurations and Moulton's Theorem in 1910

Abstract: Central configuration is a configuration of the initial positions of n bodies which satisfies a nonlinear algebraic equation system. The question on the number of central configurations for given a mass vector is one of challenge problems for 21st century's mathematicians. The exact number of central configurations for 4-body problem is still unknown. In the joint work with Mervin Woodlin, we investigate the central configurations of collinear n-body with general homogenous potential by a method involving analysis skills of some elementary algebra and calculus. It is well known that for each fixed ordered n positive masses there is exactly one collinear central configuration in the Newton's law of gravitation (F. R. Moulton, The straight line solutions of the problem of N bodies, Ann. Math., II. Ser. 12, 1910) and Smale reconfirmed the result by a variational method in 1970. However, it is not true that there is always a position which causes a central configuration for any given ordered particles with some positive masses,  and there may exists more than one position which make it central for some homogenous potential. We give a generalization of Moulton's theorem for collinear n-body problem with general homogenous potential.

In the talk, a brief introduction and background will be given in the undergraduate level. Students with some basic knowledge on linear algebra and differential equations are encouraged to attend.