The existence and stability of steady configurations in the problem of the motion of a wire triangle and a point mass under the mutual attraction*

The plane problem of the motion of a triangle, the mass of which is distributed along its sides and a point mass under the mutual attraction is investigated. The steady rotating configurations of such a system are found and the conditions for their stability and bifurcation are investigated. Configurations for which the particle is sufficiently removed from the triangle and located on the axis of symmetry opposite a vertex are found to be stable.