Continuation and bifurcations of concave central configurations in the four and five body-problems for homogeneous force laws

Santos, Alan Almeida; Marchesin, Marcelo; Pérez‐Chavela, Ernesto; Vidal, Cláudio

doi:10.1016/j.jmaa.2016.09.055

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Introduction and Statement Of The Main Results1

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Cited by 6 publications

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“…Of course, this question can be extended naturally for a > 0, see [3]. Other works that have considered power-law potentials are [7,12,15,37,38]. Albouy in [3] reinforces the role of the exponent in several of his results.…”

Section: Introduction and Statement Of The Main Resultsmentioning

confidence: 90%

On the uniqueness of the isosceles trapezoidal central configuration in the 4-body problem for power-law potentials

2019

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In this article we study the planar 4-body problem under homogeneous power-law potentials where the interaction between the bodies is given by r −a , a 4/3 (the Newtonian case corresponding to a = 3 and the vortex problem corresponding to a = 2). We study convex central configurations assuming two pairs of positive equal masses located at two adjacent vertices of a convex quadrilateral. Under these assumptions we prove that the isosceles trapezoid is the unique central configuration for every a 4/3. For the case 0 < a < 4/3, which is more difficult to study analytically, we present some numerical considerations.

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