Numerical exploration of commensurable periodic solutions of the restricted problem of three bodies and their stability

The long period problem provides the initial conditions for numerical computation of close periodic solutions separated in three categories. For each type of commensurability a number of periodic solutions are computed and their stability is studied by computing the characteristic exponents of the matrizant. The Runge-Kutta method for the solution of differential equations of motion was used in all cases. The results obtained are presented for a four cases of commensurability.