Central configurations of identical masses lying along curves

Abstract

A central configuration is an arrangement of point masses in which the net gravitational accelerations are proportional to the displacements from the center of mass. Here several families of central configurations are described consisting of a large number of identical masses that occupy one or more curves. The families are found numerically. These central configurations are regular, an algebraic condition that assures their persistence in the presence of small perturbing forces such as external fields or tethering forces. Both planar and nonplanar families exist; the planar central configurations are associated with (unstable) periodic solutions to the n -body problem. Similar configurations are exhibited for objects having pairwise interaction proportional to d(-p) at distance d for p different from 2, such as point vortices.