The solution of the equations of motions for n gravitationally interacting bodies. The 2-body problem can be solved analytically. The 3-body problem is sufficiently complicated that only the planar restricted case can be simply treated. Painlevé Eric Weisstein's World of Biography showed that there are no oscillatory solutions such that
approaches infinity while the superior limit of the minimum spacing between particles remains positive. Eric Weisstein's World of Math Painlevé Eric Weisstein's World of Biography also proved that the n-body problem has a singularity at iff
where
and
Many-Body Problem, Painlevé Problem, Three-Body Problem, Two-Body Problem
References
Meyer, K. R. Periodic Solutions of the N-Body Problem. Berlin: Springer-Verlag, 1999.
Saari, D. G. "A Visit to the Newtonian N-Body Problem via Elementary Complex Variables." Amer. Math. Monthly 97, 105-119, 1990.
Saari, D. and Xia, Z. "Off to Infinity in Finite Time." Notices Amer. Math. Soc. 42, 538-546, 1995.
