The sufficient and necessary conditions, the existence and uniqueness of a new class of central configuration in R^3, for the conjugate-nest consisting of two regular tetrahedrons, are proved. If the configuration is ...The sufficient and necessary conditions, the existence and uniqueness of a new class of central configuration in R^3, for the conjugate-nest consisting of two regular tetrahedrons, are proved. If the configuration is a central configuration, then all masses of outside layer are equivalent, and the masses of inside layer are also equivalent. At the same time p （the ratio of the sizes） and mass ratio τ=m^/m must be satisfied by some formulas. For any radius ratios ρ∈（0, 0.152996 918 2） or （0.715 223 148 7, 1.398 165 037）, there is only one central configuration. Otherwise, for any given mass ratio τ, there may exist more than one central configuration.展开更多
基金Funded by Natural Science Foundation of China (No. 10231010)KJ of Chongqing Educational Committee (No.KJ071105)and Chongqing Three Gorges University (No. SXXYYB07004).
文摘The sufficient and necessary conditions, the existence and uniqueness of a new class of central configuration in R^3, for the conjugate-nest consisting of two regular tetrahedrons, are proved. If the configuration is a central configuration, then all masses of outside layer are equivalent, and the masses of inside layer are also equivalent. At the same time p （the ratio of the sizes） and mass ratio τ=m^/m must be satisfied by some formulas. For any radius ratios ρ∈（0, 0.152996 918 2） or （0.715 223 148 7, 1.398 165 037）, there is only one central configuration. Otherwise, for any given mass ratio τ, there may exist more than one central configuration.
