Astronomy and Astrophysics – Astronomy
Scientific paper
Sep 1990
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1990cemda..50..251c&link_type=abstract
Celestial Mechanics and Dynamical Astronomy, Volume 50, Issue 3, pp.251-281
Astronomy and Astrophysics
Astronomy
Periodic Orbits, Bifurcations, Spiral Characteristics, Lagrangian Points
Scientific paper
When the Lagrangian points L4, LS in a rotating dynamical system become unstable (at a critical perturbation ɛ = ɛ,) the characteristics of some families of orbits bifurcating from the short and long period orbits (SPO and LPO) become spiral. For a given e, slightly larger than e,, an infinity of families of multiplicities n, n + 1, n + 2, n. do not bifurcate any more from SPO or LPO but join each other into a spiral. As e increases this spiral is joined by lower multiplicity families, until the SPO-LPO family itself joins the spiral. Further spirals with the same or different focuses are formed by joining other sequences of families of order n, n + l, n + 2, n, or n, n + 2, n + 4, n... Other spirals are generated at particular values of ɛ, starting and terminating at the same focus or two different focuses. As the perturbation e increases such spiral characteristics join other families, away from the focus. The orbits along the spiral characteristics have an increasing number of loops (either n, n + 1, n + 2, ..., or n, n + 2, n + 4 n.) around, or close to L4. In the first case the loops are along the symmetry axis, passing through L 4. In the second case the loops appear in pairs outside the symmetry axis. The focuses correspond to homoclinic, or heteroclinic orbits, spiralling around L 4 and /or L 5.
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