Stability of and motion aboutL4 at three-to-one commensurability

The stability of L4 and the motion about L4 in the restricted problem of three bodies is investigated when there is three-to-one commensurability between the long and short periods of motion, that is, when the mass ratio has the value =0.013516.... The two time scale method is used (1) to show that L4 is an unstable equilibrium point when =3, (2) to determine for what initial conditions periodic orbits occur when 3, (3) to determine the stability of the periodic orbits, and (4) to investigate the boundedness of the motions about L4 when 3. 1971 D. Reidel Publishing Company.

Stability of and motion aboutL4 at three-to-one commensurability Academic Article