Regularization of partial collisions in the \(N\)-body problem
A simultaneous collision in the \(N\)-body system is studied. By suitable coordinate and time transformations, the equations of motion are regularized relative to the \(n\)-collision (\(2\leq n\leq N\)). A qualitative study is performed and some asymptotic results concerning the ultimate behavior of the partial collapse solutions tending to the set of central configurations are obtained. It is proved that a certain set of equilibrium points is attractive for the partial collision orbits of motion, and that the sufficiently hyperbolic partial collapse solutions can be \(C^ 1\)-regularized with respect to the new time variable.
scientific article; zbMATH DE number 90478