Abstract
The study of a dynamical system comprises a variety of processes, each one of which requires careful analysis. A fundamental preliminary step is to detect and limit the regions where solutions may exist. In the case of the ring problem of (N+1)-bodies or, otherwise, the regular polygon problem of (N+1) bodies, the existence of a Jacobian-type integral of motion constitutes the key for the investigation of the areas where the motions of the small particle are realized. Based on the aforementioned integral, we present an extended study of the parametric evolution of the regions where 3-D particle motions may exist.
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