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The optimal upper bound of the number of generalized Euler configurations |
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| Authors: | LI ZhengDong & FU YanNing Purple Mountain Observatory Chinese Academy of Sciences Nanjing China Graduate University of Chinese Academy of Sciences Beijing |
| Affiliation: | 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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