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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
Universitat de Vic. Escola Politècnica Superior; Universitat de Vic. Grup de Recerca en Tecnologies Digitals
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.
First published in The Proceedings of the American Mathematical Society in Volume 133, Number 2, p. 529-536 published by the American Mathematical Society
Tots els drets reservats
8 p.
American Mathematical Society

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