Stability and branching of stationary rotations in a planar problem of motion of mutually gravitating triangle and material point

The planar motion of an equilateral triangle with equal masses at vertices and of a point subjected to mutual Newtonian attraction is considered. Necessary conditions for the stability of “straight”, axial steady configurations, when the massive point is located on one of the symmetry axes of the triangle, are studied. The generation of other, “oblique”, steady configurations is discussed in connection with the variation, for certain parameter values, of the degree of instability of some “straight” steady configurations.