Analytical solution to the three-body problem for a two-frequency resonance system of the first order.

Details Analytical solution to the three-body problem for a two-frequency resonance system of the first order. Analytical solution to the three-body problem for a two-frequency resonance system of the first order.

Feb 1995

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1995sosyr..29...41m&link_type=abstract

Solar System Research, Vol. 29, No. 1, p. 41 - 51

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Three-Body Problem: Resonances

Scientific paper

The evolution of a two-frequency dynamic system is investigated within the framework of a spatial three-body problem at first-order commensurability. The mass of one of the bodies greatly exceeds that of the others. Zeipel's asymptotical method was applied to solve the problem of small mutual inclinations and eccentricities of the bodies. An analytical solution, which describes the evolution of all orbital elements of the gravitating bodies, is obtained in terms of the Weierstrass functions.

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