Abstract
The N -body ring problem is a classical problem that describes the motion of particle attracted by the gravitational field of N + 1 primary bodies. These bodies are distributed in a planar ring configuration, that is, a central primary and N primaries of equal mass located at the vertices of a regular polygon that is rotating on its own plane about the center with a constant angular velocity. If N is large enough, this system models the motion of a small particle close to a planetary ring. The study of the escape of a particle from the potential well of this system requires the use of very accurate numerical integration methods, as we are interested in the integration of the problem over very long spans of time, and large values of N . In this paper, we analyze the integration of the equations of motion of this problem by recurrent power series, and compare the resulting numerical solutions against some other methods.
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