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The number of planar central configurations for the 4-body problem is finite when 3 mass positions are fixed

The number of planar central configurations for the 4-body problem is finite when 3 mass positions are fixed
 
Alvarez, Martha ; Corbera Subirana, Montserrat ; Delgado, Joaquin ; Llibre, Jaume
2005

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Abstract

In the n{body problem a central con guration is formed when the position vector of each particle with respect to the center of mass is a common scalar multiple of its acceleration vector. Lindstrom showed for n = 3 and for n > 4 that if n 􀀀? 1 masses are located at xed points in the plane, then there are only a nite number ...»»»»
In the n{body problem a central con guration is formed when the position vector of each particle with respect to the center of mass is a common scalar multiple of its acceleration vector. Lindstrom showed for n = 3 and for n > 4 that if n 􀀀? 1 masses are located at xed points in the plane, then there are only a nite number of ways to position the remaining nth mass in such a way that they de ne a central con guration. Lindstrom leaves open the case n = 4. In this paper we prove the case n = 4 using as variables the mutual distances between the particles.^^^^

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First published in The Proceedings of the American Mathematical Society in Volume 133, Number 2, p. 529-536 published by the American Mathematical Society
 
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Citation:

ALVAREZ, M. i altres . "The number of planar central configurations for the 4-body problem is finite when 3 mass positions are fixed". A: Proceedings of the American Mathematical Society, 2005, vol. 133, núm. 2, pàg. 529-536.
 
 
 
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