Seminar

For the planar three body problem with a-homogeneous potential (1/r^a), when two of the masses are equal, using action minimization method, we show that for 1<a<2, there is a collision-free periodic solution, whose projection in the shape space looks like a figure 8; for a=1(the Newtonian potential), the minimizer is either a collision-free periodic solution as above, or it is a Schubart solution (a collinear periodic solution containing binary collisions).