caa a22 4500 467987173 CHVBK 20180323112535.0 cr unu---uuuuu 170328e19900901xx s 000 0 eng 10.1007/BF00048767 doi (NATIONALLICENCE)springer-10.1007/BF00048767 Contopoulos G. University of Florida, 32611, Gainesville, FL., U.S.A. aut The generation of spiral characteristics [Elektronische Daten] [G. Contopoulos] When the Lagrangian points L4, LS in a rotating dynamical system become unstable (at a critical perturbation ε = ε,) 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 ε, 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. Kluwer Academic Publishers, 1991 Periodic orbits nationallicence bifurcations nationallicence spiral characteristics nationallicence Lagrangian points nationallicence Celestial Mechanics and Dynamical Astronomy Kluwer Academic Publishers 50/3(1990-09-01), 251-281 0923-2958 50:3<251 1990 50 10569 https://doi.org/10.1007/BF00048767 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/BF00048767 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Contopoulos G. University of Florida, 32611, Gainesville, FL., U.S.A aut NATIONALLICENCE 773 0- Celestial Mechanics and Dynamical Astronomy Kluwer Academic Publishers 50/3(1990-09-01), 251-281 0923-2958 50:3<251 1990 50 10569 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer