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Designing parallel programs and integrated circuits

Auteur(s) : P. Quinton, T. Risset, K. Morin-Allory, D. Cachera

Doc. Source: 8ème International Mathematica Symposium (IMS'06)

Publisher : IEEE

Pages : 1-13

The study of central configurations of the Newtonian many-body problem is a very old problem in Celestial Mechanics. Many papers have been devoted to its investigation and many interesting results have been obtained (see, for example, [1]). One of the reasons why central configurations are important and interesting is that every such configuration generates an exact homographic solution of the corresponding n-body problem [2]. For example, two bodies form only one central configuration and general solution of the two-body problem is just a homographic one. In the case of n=3 there exist five central configurations which have been found by Lagrange and Euler yet. One can be easily shown analytically that there are not any other central configuration of three bodies. But for n≥4 the problem of existence of central configurations is much more complicated. Even for n=4 it is not known how many central configurations exist and what shapes do they have.