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The optimal upper bound of the number of generalized Euler configurations
Authors:LI ZhengDong    & FU YanNing Purple Mountain Observatory  Chinese Academy of Sciences  Nanjing  China  Graduate University of Chinese Academy of Sciences  Beijing
Institution:LI ZhengDong 1,2,& FU YanNing 11 Purple Mountain Observatory,Chinese Academy of Sciences,Nanjing 210008,China,2 Graduate University of Chinese Academy of Sciences,Beijing 100039
Abstract:Consider a generalized 3-body problem. The attraction force between any two bodies is proportional to the two masses and the b-th power of the mutual distance. Albouy and Fu have obtained the optimal upper bound of the number of generalized Euler configurations for the cases b 1 and b = 2, 3. This paper obtains the optimal upper bound for the remaining real values of b in a systematic way.
Keywords:three-body problem  central configuration  generalized Euler configuration  quasi-polynomial equation  
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