2010
DOI: 10.1007/s10569-010-9291-5
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Central configurations for the planar Newtonian four-body problem

Abstract: Planar central configurations of four different masses are analyzed theoretically and computed numerically. We follow Dziobek's approach to four-body central configurations with a straightforward implicit (in the masses and distances) method of our own in which the fundamental quantities are each the quotient of a directed area divided by the corresponding mass. We apply a new simple numerical algorithm to construct general fourbody central configurations. We use this tool to obtain new properties of the symme… Show more

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Cited by 18 publications
(22 citation statements)
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“…Also considering the particles endowed with masses and charges, Alfaro and Perez-Chavela (2002) proved the existence of a continuum of central configurations in a particular 4-body problem. Other recent papers on central configurations are due to Corbera, Cors and Llibre (2010), , Gidea and Llibre (2010), Piña and Lonngi (2010), ... Recently the first and second author of this paper gave new examples of stacked central configurations of the 5-bodies which, as the ones studied by Hampton (2005), have three bodies in the vertices of an equilateral triangle, but the other two are on the perpendicular bisector (Llibre and Mello 2008).…”
Section: Introductionmentioning
confidence: 93%
“…Also considering the particles endowed with masses and charges, Alfaro and Perez-Chavela (2002) proved the existence of a continuum of central configurations in a particular 4-body problem. Other recent papers on central configurations are due to Corbera, Cors and Llibre (2010), , Gidea and Llibre (2010), Piña and Lonngi (2010), ... Recently the first and second author of this paper gave new examples of stacked central configurations of the 5-bodies which, as the ones studied by Hampton (2005), have three bodies in the vertices of an equilateral triangle, but the other two are on the perpendicular bisector (Llibre and Mello 2008).…”
Section: Introductionmentioning
confidence: 93%
“…The four-body problem. Although unsolved problems remain, for the Newtonian (A = 3) and vortex case (A = 2) of the four-body problem the central configurations are well understood, with many particular results for configurations with some special symmetry or other properties [77,39,86,49,15,104,54,84,55,61,75,108,9,62,110,128,35,143,11,18,63,43,37,46,30,122]. The equal mass case is especially well characterized.…”
Section: 2mentioning
confidence: 99%
“…In order to prove that these equations are equivalent to the equations defining the central configurations, we need the planar conditions [7], [8]…”
Section: Central Configurations Of 4 Massesmentioning
confidence: 99%