Central configurations for the planar Newtonian Four-Body problem

Details Central configurations for the planar Newtonian Four-Body problem Central configurations for the planar Newtonian Four-Body problem

2009-05-27

arxiv.org/abs/0905.4329v1

Physics

Mathematical Physics

24 pages, 2 figures, files included in zip: PinaLonngi.tex, concave.ps, convexe.ps

Scientific paper

The plane case of central configurations with four different masses is analyzed theoretically and is computed numerically. We follow Dziobek's approach to four body central configurations with a direct implicit method of our own in which the fundamental quantities are the quotient of the directed area divided by the corresponding mass and a new simple numerical algorithm is developed to construct general four body central configurations. This tool is applied to obtain new properties of the symmetric and non-symmetric central configurations. The explicit continuous connection between three body and four body central configurations where one of the four masses approaches zero is clarified. Some cases of coorbital 1+3 problems are also considered.

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