A Class of Pyramidal Central Configurations with Logarithmic Potentials
Journal: Journal of Higher Education Research DOI: 10.32629/jher.v5i6.3420
Abstract
It is well known that for the pyramidal central configuration of the five-body problem, four masses are located at the vertices of the square and the fifth mass is located on a line perpendicular to the plane containing the square. And the line passes through the geometric center of the square. If the potential is Newtonian, then the values of the four masses at the vertices of the square are equal. In this paper, by using some properties of circulant matrices, we find that if the potentials are logarithmic potentials, then the values of the four masses are equal, too.
Keywords
n-body problem, pyramidal central configurations, logarithmic potentials, circulant matrices
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[3] Perko L, Walter E. 1985. Regular polygon solutions of the N-body problem. Proceedings of the American Mathematical Society, 1985, 94(2): 301-309.
[4 ]Wang Z. 2019. Regular polygon central configurations of the N-body problem with general homogeneous potential. Nonlinearity 2019, 32(7): 2426-2440.
[5] Ouyang T, Xie Z, Zhang S. 2004. Pyramidal central configurations and perverse solutions. Electronic Journal of Differential Equations, 2004(106): 1-9.
[6] Fayҫal N. 1996. On the classification of pgramidal central configurations. Proceedings of the American Mathematical Society, 124(1): 249-258.
[7] Wintner A. 1941. The analytical foundations of celestial mechanics. Princeton: Princeton University Press.
[8] Marcus M, Minc H. 1964. A survey of matrix theory and matrix inequalities. Boston: Allyn and Bacon.
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