Bifurcation of separatrices in the averaged planetary three-body problem with first and second order resonances.

Details Bifurcation of separatrices in the averaged planetary three-body problem with first and second order resonances. Bifurcation of separatrices in the averaged planetary three-body problem with first and second order resonances.

Jan 1994

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1994sosyr..27..382s&link_type=abstract

Solar System Research, Vol. 27, No. 4, p. 382 - 387

Physics

Three-Body Problem: Resonances

Scientific paper

The stability of the motions in the mean unbounded three-body problem with two-frequency resonances of first and second order is investigated. Equations of motion are obtained near the resonance surface for the case of the mean plane unbounded planetary three-body problem with first-order resonance and the circular case of the mean three-dimensional unbounded planetary three-body problem with second-order resonance. Analytic conditions for libration of the resonant phase are found. With the help of the separatrices a qualitative picture is constructed for the behavior of solutions in the phase plane. The dependence of separatrix bifurcation on an analytic parameter is investigated.

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