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Central configurations with many small masses. (English) Zbl 0724.70015
Summary: By using the method of analytical continuation, we find the exact numbers of central configurations for some open sets of n positive masses for any choice of n. It turns out that the numbers increase dramatically as n increases; e.g., for some open set of 18 positive masses, some 2·08766×10 20 classes of distinctive central configurations are found. In the mean time, we obtained some results about the Hausdorff measure for the set of n positive masses where degenerate central configuration arises.
MSC:
70G10Generalized coordinates; event, impulse-energy, configuration, state, or phase space
70F10n-body problems
70-08Computational methods (mechanics of particles and systems)