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Isosceles trapezoid central configurations of the Newtonian four-body problem

Published online by Cambridge University Press:  07 June 2012

Zhifu Xie
Affiliation:
Department of Mathematics and Computer Science, Virginia State University, Petersburg, Virginia 23806, USA ([email protected])

Abstract

We use a simple direct and basic method to prove that there is a unique isosceles trapezoid central configuration of the planar Newtonian four-body problem when two pairs of equal masses are located at adjacent vertices of a trapezoid. Such isosceles trapezoid central configurations are an exactly one-dimensional family. Explicit expressions for masses are given in terms of the size of the quadrilateral.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 2012

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