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Collinear central configurations in the n-body problem with general homogeneous potential
J. Math. Phys. 50, 102901 (2009); doi:10.1063/1.3205451
Published 16 October 2009
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In this paper we investigate the central configurations of collinear n-body problem given by the general law of attraction of the form f(r)=1/r
. A method involving analysis skills of some elementary algebra and calculus is presented to study the central configurations in the collinear n-body problem. It is well known that for given n positive masses, there are precisely n!/2 collinear central configurations for Newton's law of gravitation of 
=2. However, it is not true that there is always a position that causes a central configuration for any given ordered particles with some positive masses and that there may exist more than one position that make it central for some <0. We give a generalization of Moulton's theorem for collinear n-body problem for all >0. Examples that Moulton's theorem does not work are also provided.
©2009 American Institute of Physics
. A method involving analysis skills of some elementary algebra and calculus is presented to study the central configurations in the collinear n-body problem. It is well known that for given n positive masses, there are precisely n!/2 collinear central configurations for Newton's law of gravitation of =2. However, it is not true that there is always a position that causes a central configuration for any given ordered particles with some positive masses and that there may exist more than one position that make it central for some <0. We give a generalization of Moulton's theorem for collinear n-body problem for all >0. Examples that Moulton's theorem does not work are also provided.
©2009 American Institute of Physics
| History: | Received 11 June 2009; accepted 23 July 2009; published 16 October 2009 |
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http://link.aip.org/link/?JMAPAQ/50/102901/1 |
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