Two cases of the nested configurations in R^3 consisting of two regular quadrilaterals are discussed. One case of them do not form central configuration, the other case can be central configuration. In the second case...Two cases of the nested configurations in R^3 consisting of two regular quadrilaterals are discussed. One case of them do not form central configuration, the other case can be central configuration. In the second case the existence and uniqueness of the central configuration are studied. If the configuration is a central configuration, then all masses of outside layer are equivalent, similar to the masses of inside layer. At the same time the following relation between r(the ratio of the sizes) and mass ratio b = m/m must be satisfied b=24(3的立方根)（3r^2+2r+3）^-3/2-8（1-r）|1-r|^-3-3(6r的立方根)/24(3的立方根)（3+r）（3r^2+2r+3）^-3/2-8r（1-r）|1-r|^-3-3(6r^-2的立方根)in which the masses at outside layer are not less than the masses at inside layer, and the solution of this kind of central configuration is unique for the given ratio (b) of masses.展开更多
基金Supported by the NSF of China(10231010)Supported by the NSF of CQSXXY (20030104)
文摘Two cases of the nested configurations in R^3 consisting of two regular quadrilaterals are discussed. One case of them do not form central configuration, the other case can be central configuration. In the second case the existence and uniqueness of the central configuration are studied. If the configuration is a central configuration, then all masses of outside layer are equivalent, similar to the masses of inside layer. At the same time the following relation between r(the ratio of the sizes) and mass ratio b = m/m must be satisfied b=24(3的立方根)（3r^2+2r+3）^-3/2-8（1-r）|1-r|^-3-3(6r的立方根)/24(3的立方根)（3+r）（3r^2+2r+3）^-3/2-8r（1-r）|1-r|^-3-3(6r^-2的立方根)in which the masses at outside layer are not less than the masses at inside layer, and the solution of this kind of central configuration is unique for the given ratio (b) of masses.
