Central Configuration And Periodic Solution Of N-body Problem

N-body problem is a system of O.D.E.. It reads the law of N bodies. In general, N-body problem is the research which the N bodies move under the Newtonian law and the law of gravity. Without doubt, the Newtonian law very appropriately reads the moving law of the solar system. In the research of the N-body problem, Central Configuration is an important content From it, we can obtain periodic solution; it has close connection with collision or escaping. The following are some classical results: For three bodies of arbitrary mass,the Central Configuration has only collinear or equilateral triangle; For four bodies of arbitrary mass,the non-planar Central Configuration has only tetrahedron;in 1985, L.M.Perko and E.L.Walter discovered that placing a mass at every point of regular n-gons,they can form Central Configuration iff the masses equal each other;in 1995, R.Moechel and C.Simo discovered the sufficient and necessary conditions of C.Cs which formed by two layers of regular n-gons,the two n-gons don't have to equal,but the directions must be the same.In 2002,the author have discovered existence, uniqueness or the sufficient and necessary conditions of several C.Cs with his supervisor.Theory 1 implies the existence of C.C. consisted of two twisted layers n-gons. Theory 2 implies the sufficient and necessary conditions of C.C. consisted of nested Tetrahedrons .Theory 3 implies the sufficient and necessary conditions of C.C. consisted of nested .Theory 4 implies a kind of periodic solution doesn't exist.