Some Problems In N-body Central Configurations

Central configuration is an important concept in celestial mechanics. It is such a kind of configuration q = (q~,. . . ,qn) ~ (R~ that when the n mass points with masses m~ located at qj are released with zero velocity, they will simultaneously collide under the action of Newton universal gravity. A natural question on central configuration mentioned in the famous book of A.Wintner published in 1941 is that, for the given masses, what is the number of them? This is such a difficult problem that it is still open now.In this thesis, we will follow two lines to study such a problem. In the second part, we consider non-collinear central configurations in planar 4-body problem. Under some special mass cases, we get the symmetry and the shape of the central configurations. In the third and fourth parts, we consider the sufficient and necessary condition when a configuration is a central one for some mass vectors. Firstly, we give an equivalent characterization for the given configuration to be a central one. Then we use this simple formulation to give a unifying proof for the known results and study some new configurations. We also study the properties of central configurations with some equal edges in the planar 4-body problem. The first part is the introduction on the literature and our results in details.