Two Central Configuration Problems Consisting Of Regular N-gon Under Logarithmic Potential

Collision problem is a fundamental problem in the Newton N-body problem-s.It is important to find the central configuaration because it is the limiting configuration of collision.Finiteness of central configurations is listed as one of the 18 important mathematical problems in the 21st century by mathematician Smale.In this thesis,the central configuration problems consisting of regular n-gon are discussed under logarithmic potential.In chapter 2,first,the existence of the center configuration of a double-layer regular n-gon is discussed by algebraic and analytic methods.For the double-layer regular n-gon configura-tion,if the two regular n-gon have the same size and the masses of each body on vertex are equal,it is obtained that there exists a unique central configuration when the potential is log-arithmic potential and its twisted angle is ?/n.Then,the double-layer square configuration is discussed.Based on similar conditions,it is obtained that there exists a unique central config-uration when its twisted angle is 0 or ?/4.In chapter 3,the necessary condition for the central configuration of a class of double-layer square is discussed by algebraic and analytic methods.If the bodies at the vertices of the same square have equal masses and the potential is logarithmic potential,the necessary condition on which the two squares to form a central configuration is that its twisted angel is equal to k?/2 or (k?/2 + ?/4).