| Summary: | 碩士 === 國立中山大學 === 應用數學系研究所 === 105 === The central configuration motion, listed as one of problems for the twenty-first century, is the N-body Newtonian motion along which the net force on each body by all the other bodies always points to the center of mass and is proportional to the distance to the center of mass. The problem leads to the study of the behavior of solutions near collisions and the N-body dynamics.
While computing the planar central configuration motion by classical numerical methods is always unstable except for two body system. To overcome this difficulty, for each mass we introduce its corresponding virtual mass so that the motion of N-body central configuration is reduced to N two-body motions, which is quite stable by using the classical numerical methods such as Runge-Kutta method.
Once the two-body motion is confirmed, the trajectory of the motion must be an ellipse by Kepler''s laws. Thus, we can construct the circumcircle of the ellipse to derive the relation of true anomaly and eccentric anomaly by Kepler''s equation, from which the solution of the two-body problem can be achieved.
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