Mathematics
Scientific paper
Jul 1993
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1993avest..27..109s&link_type=abstract
Astronomicheskii Vestnik (ISSN 0320-930X), vol. 27, no. 4, p. 109-115
Mathematics
2
Branching (Mathematics), Orbital Resonances (Celestial Mechanics), Three Body Problem, Equations Of Motion, Libration, Orbital Mechanics
Scientific paper
The stability of the motion in the averaged general three-body problem in the case of the first-order and second-order two-frequency resonances is investigated. For the case of the averaged planar general three-body problem at the first-order resonance and the circular case of the averaged spatial general three-body problem at the second-order resonance the equations of motion of bodies near the resonance surface are derived. The analytical condition of the liberation of the resonance phase is obtained. With the help of separatrices the qualitative picture of the solution's dynamics is constructed on the phase plane. The bifurcation of separatrices is researched with respect to some parameter which is analytically found.
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