Under the necessary conditions for a double pyramidal central configuration with a diamond base to exist in the real number space, the existence and uniqueness of such configurations were studied by employing combined...Under the necessary conditions for a double pyramidal central configuration with a diamond base to exist in the real number space, the existence and uniqueness of such configurations were studied by employing combinedly the algebraic method and numerical calculation. It is found that there exists a planar curl triangle region G in a square Q such that any point in G and given by the ratio of the two diagonal lengths of the diamond base and the ratio of one diagonal length of the base to the height of the double pyramid configuration determines a unique double pyramid central configuration, while all points in Q-G have no referance to any central configuration.展开更多
Based on some necessary conditions for double pyramidal central configurations with a concave pentagonal base, for any given ratio of masses, the existence and uniqueness of a class of double pyramidal central configu...Based on some necessary conditions for double pyramidal central configurations with a concave pentagonal base, for any given ratio of masses, the existence and uniqueness of a class of double pyramidal central configurations with a concave pentagonal base in 7-body problems are proved and the range of the ratio between radius and half-height is obtained, within which the 7 bodies involved form a central configuration or form uniquely a central configuration.展开更多
On some necessary conditions for double pyramidal central configurations with concave heptagon for any given ratio of masses, the existence and uniqueness of a class of double pyramidal central configurations with con...On some necessary conditions for double pyramidal central configurations with concave heptagon for any given ratio of masses, the existence and uniqueness of a class of double pyramidal central configurations with concave heptagon base for nine-body problems is proved in this paper, and the range of the ratio cr of the circularity radius of the heptagon to the half-height of the double pyramidal central configuration involved in this class configurations is obtained, which is in the interval （√3/3,1.099 600 679）, and the configuration involved in the bodies with any σ∈ （√3/3, 1.099 600 679） can form a central configuration which is a uniquely central configuration is proved.展开更多
文摘Under the necessary conditions for a double pyramidal central configuration with a diamond base to exist in the real number space, the existence and uniqueness of such configurations were studied by employing combinedly the algebraic method and numerical calculation. It is found that there exists a planar curl triangle region G in a square Q such that any point in G and given by the ratio of the two diagonal lengths of the diamond base and the ratio of one diagonal length of the base to the height of the double pyramid configuration determines a unique double pyramid central configuration, while all points in Q-G have no referance to any central configuration.
基金Natural Science Foundation of China (No.19871096)
文摘Based on some necessary conditions for double pyramidal central configurations with a concave pentagonal base, for any given ratio of masses, the existence and uniqueness of a class of double pyramidal central configurations with a concave pentagonal base in 7-body problems are proved and the range of the ratio between radius and half-height is obtained, within which the 7 bodies involved form a central configuration or form uniquely a central configuration.
基金Funded by NSF (Natural Science Foundation) of China (No. 10231010) and NSF of Chongqing Educational Committee (KJ051109, KJ06110X), NSF of Chongqing Science and Technology Committee, NSF of CQSXXY
文摘On some necessary conditions for double pyramidal central configurations with concave heptagon for any given ratio of masses, the existence and uniqueness of a class of double pyramidal central configurations with concave heptagon base for nine-body problems is proved in this paper, and the range of the ratio cr of the circularity radius of the heptagon to the half-height of the double pyramidal central configuration involved in this class configurations is obtained, which is in the interval （√3/3,1.099 600 679）, and the configuration involved in the bodies with any σ∈ （√3/3, 1.099 600 679） can form a central configuration which is a uniquely central configuration is proved.
