The stellar three-body problem

Two applications of von Zeipel's method to the stellar three-body problem eliminate the short period terms and establish two new integrals of the motion beyond the classical integrals. The remaining time averaged problem with only the second order Hamiltonian has one additional integral and can be solved. The motion with the third order averaged Hamiltonian included is more complex, in that there may be additional resonances, and the additional integral does not exist in all cases.