On the central configurations of the planar 1 + 3 body problem
We consider the Newtonian four-body problem in the plane with a dominat mass M. We study the planar central configurations of this problem when the remaining masses are infinitesimal. We obtain two different classes of central configurations depending on the mutual distances between the infinitesimal masses. Both classes exhibit symmetric and non-symmetric configurations. And when two infinitesimal masses are equal, with the help of extended precision arithmetics, we provide evidence that the number of central configurations varies from five to seven.
Keywords1 + 3 body problem Central configurations Coorbital satellites
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- Hall, G.R.: Central configurations in the planar 1 + n body problem, Preprint (1988)Google Scholar
- Maxwell, J.C.: On the stability of the motion of Saturn’s rings. In: Maxwell on Saturn’s Rings, pp 69–158. MIT Press (1859)Google Scholar
- Olver P.: Classical invariant Theory, London Mathematical Society Student Texts, vol. 44. Cambridge University Press, New York (1999)Google Scholar