立方体套中心构型的存在唯一性(英文)

EXISTENCE AND UNIQUENESS OF EQUIVALENT CLASS OF THE CENTRAL CONFIGURATION FOR NESTED CUBES

本文研究两层立方体套中心构型,运用中心构型等价类的性质结合分析方法,得到了立方体套构成中心构型等价类的充分与必要条件,并且证明了该等价类对于任意给定的质量比具有存在唯一性,推广了文[8]的结论.

This paper studies the nested configuration consisting of two cubes. Using properties of equivalent class of central configurations and analysis method, we obtain the necessary and sufficient conditions of the central configurations of the nested cubes, and prove that the central configuration class exists and is unique for any given mass ratio. The works extend the results in [8].