On Central Configurations Of N-body Problem

Celestial mechanics is an old subject. It is a branch of astronomy, but it has intimate relationship with mathematics and mechanics. Among the modern celestial mechanics' researches, n-body problem is an important field. N-body problem is a common research between celestial mechanics and general mechanics vs. applied mathematics. Central configuration which has a history more than 100 years is an important tool to study n-body problem , and the famous mathematician Stave Smale once described it one of the 10 important mathematics problems in 21 century.In this thesis, we find a kind of special compound central configuration which is composed of regular hexahedron and regular octahedron, and also we study the necessary and sufficient conditions for regular hexahedron and regular octahedron to form a central configuration. In addition, from the square central configuration, under the conditions that the masses and places of 2 bodies on a diagonal don't change and one place of a body on the other diagonal doesn't change, we study how this kind of configuration can form central configuration and we find the sufficient and necessary conditions to form a central configuration, and also we give the numeric simulation of such a kind of central configuration.