On Central Configurations Of N-body Problem

Celestial mechanics is an old subject. It is a branch of astronomy, but it hasintimate relationship with mathematics and mechanics. Among the modern celestialmechanical researches, N-body problem is an important field. N-body problem is acommon research field of celestial mechanics, general mechanics and appliedmathematics. Central configuration which has a history of more than 100 years is animportant tool to study N-body problem, and the famous mathematician Stave Smaleonce described it one of the 10 important mathematicalproblems in 21 century. Based on the definitions of Homothetic solution,Homographic solution andcentral configuration solution, In this thesis, we discuss the classifications of centralconfigurations for two nested cubes; discuss the classifications of centralconfigurations for two nested regular octahedrons; the classifications of planar centralconfigurations consisted by two diamonds. discuss some classifications of equivalentclasses for spacial double pyramidal central configurations; such as the classificationsof equivalent classes of double pyramidal central configurations for 5-bodies witharbitrary triangle sase, the classifications of equivalent classes of double pyramidalcentral configurations for 6-bodies with parallelogram base, the classifications ofequivalent classes of double pyramidal central configurations for 7-bodies withconcave pentagon base.