Abstract
The flat central configurations of four planet motions are investigated with Wu's elimination method. We obtain 12 collinear central configurations and a necessary condition for determining flat but noncollinear central configurations. We also prove that the number of central configurations in planet motions of 4 bodies is finite under the condition that the masses and angular velocity of the planets do not satisfy any algebraic relations.
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References
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Wu Wen-tsiin, Basic Principles of Mechanical Theorem Proving in Geometries, Volume 1: Part on Elementary Geometries, Science Press, Beijing (in Chinese), 1984; English edition, Springer, Wien New York, 1994.
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© 1998 Springer-Verlag Berlin Heidelberg
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Shi, H., Zou, F. (1998). Flat central configurations of four planet motions. In: Wang, D. (eds) Automated Deduction in Geometry. ADG 1996. Lecture Notes in Computer Science, vol 1360. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0022717
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DOI: https://doi.org/10.1007/BFb0022717
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