A qualitative analysis of the plane averaged restricted three body problem

Details A qualitative analysis of the plane averaged restricted three body problem A qualitative analysis of the plane averaged restricted three body problem

Feb 1980

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1980azh....57..182v&link_type=abstract

Astronomicheskii Zhurnal, vol. 57, no. 1, 1980, p. 182-189. In Russian.

Astronomy and Astrophysics

Astronomy

Celestial Mechanics, Elliptical Orbits, Orbit Calculation, Orbit Perturbation, Qualitative Analysis, Three Body Problem, Eccentricity, Librational Motion, Orbital Elements, Polynomials

Scientific paper

A study of the properties of the perturbation function by its expansion into a converging series followed by an analysis of the series is presented. It is shown that there are three classes of solutions for orbital elements: two classes are characterized by periodic changes of eccentricity, with the pericenter of the orbit performing a libration type periodic motion in the first case, and periodically circulating in the second case. The third case is defined by an instability of the perturbed orbit, and the eccentricity reaches unity while the major axis remains constant.

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