Trajectories in the plane, circular, restricted three-body problem with a 2:1 resonance

Details Trajectories in the plane, circular, restricted three-body problem with a 2:1 resonance Trajectories in the plane, circular, restricted three-body problem with a 2:1 resonance

Oct 1983

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1983azh....60.1026g&link_type=abstract

Astronomicheskii Zhurnal, Vol. 60, p.1026

Astronomy and Astrophysics

Astronomy

3

Scientific paper

The Delaunay-Hill plane version averaging method is applied to the circular restricted three-body problem when the mean motions are close to the 2:1 commensurability. The analytical expressions for the elements h = e exp {iD}, k = e exp {-iD} where e is the eccentricity, and D the Delaunay anomaly, are obtained in terms of Weierstrass functions for the case when in the perturbation function first four terms are retained. It is shown that five different classes of trajectories can exist.

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