Stability of and motion aboutL 4 at three-to-one commensurability

Details Stability of and motion aboutL 4 at three-to-one commensurability Stability of and motion aboutL 4 at three-to-one commensurability

Sep 1971

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1971cemec...4...60a&link_type=abstract

Celestial Mechanics, Volume 4, Issue 1, pp.60-77

Physics

5

Scientific paper

The stability ofL 4 and the motion aboutL 4 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 thatL 4 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 aboutL 4 when μ≈μ3.

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