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


  • 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 μ has the value μ=μ0.013516.... The two time scale method is used (1) to show that L4 is an unstable equilibrium point when μ=μ3, (2) to determine for what initial conditions periodic orbits occur when μ≈μ3, (3) to determine the stability of the periodic orbits, and (4) to investigate the boundedness of the motions about L4 when μ≈μ3. © 1971 D. Reidel Publishing Company.

author list (cited authors)

  • Alfriend, K. T.

citation count

  • 14

publication date

  • September 1971