The plane unrestricted three-body problem

The Lagrangian coordinates of the unrestricted three-body problem with forces proportional to r_ij^α (r_ij are mutual distances between the bodies and α is an arbitrary real number not equal to -1) are chosen in such a way to make one of the equations of motion to be a Lagrange-Jacobi one. Cases of the unlimitedly increasing polar moment of inertia are specially considered. The paper contains the geometrical interpretation for the plane problem.