Abstract
When μ is smaller than Routh’s critical value μ 1 = 0.03852 . . . , two planar Lyapunov families around triangular libration points exist, with the names of long and short period families. There are periodic families which we call bridges connecting these two Lyapunov families. With μ increasing from 0 to 1, how these bridges evolve was studied. The interval (0,1) was divided into six subintervals (0, μ 5), (μ 5, μ 4), (μ 4, μ 3), (μ 3, μ 2), (μ 2, μ 1), (μ 1, 1), and in each subinterval the families B(pL, qS) were studied, along with the families B(qS, qS′). Especially in the interval (μ 2, μ 1), the conclusion that the bridges B(qS, qS′) do not exist was obtained. Connections between the short period family and the bridges B(kS, (k + 1)S) were also studied. With these studies, the structure of the web of periodic families around triangular libration points was enriched.
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Hou, X.Y., Liu, L. On bridges B(pL, qS) around triangular libration points. Celest Mech Dyn Astr 104, 241–256 (2009). https://doi.org/10.1007/s10569-009-9206-5
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DOI: https://doi.org/10.1007/s10569-009-9206-5