Parametric stability analysis for planar bicircular restricted four-body problem
bicircular four-body model, parametric resonance, libration points
Stability for the non-autonomous bicircular four-body model is analytically investigatedin this study. The governing equation is derived from Newton’s law of gravity. Whenthe distance between the infinitesimal mass and the third primary is expanded as Taylorexpansions, the governing equation can be regarded as two parts: the unperturbedconservative system and the small periodically parametric excitations. The unperturbedsystem’s natural frequency and parametric frequency are analyzed for the possibility ofprincipal parametric resonances. The method of multiple scales is applied directly to thegoverning equation. The stability conditions are obtained analytically for the principalparametric resonance. Numerical method demonstrates the efficiency of the analyticalresults.
Tsinghua University Press
Ying-Jing Qian, Lei-Yu Yang, Xiao-Dong Yang et al. Parametric stability analysis for planar bicircular restricted four-body problem.Astrodyn.2018, 2(2): 147–159.