Problem of the translational-rotational motion of three gravitating bodies

Details Problem of the translational-rotational motion of three gravitating bodies Problem of the translational-rotational motion of three gravitating bodies

Sep 1978

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1978kosis..16..665e&link_type=abstract

Kosmicheskie Issledovaniia, vol. 16, Sept.-Oct. 1978, p. 665-669. In Russian.

Physics

1

Celestial Mechanics, Rotating Bodies, Three Body Problem, Translational Motion, Canonical Forms, Fourier Series, Gravitational Effects, Series Expansion, Spheres, Steady State

Scientific paper

In the present paper, the problem of translational-rotational motion of three mutually attracting bodies is formulated. It is assumed that two of the bodies are spheres with a radial density distribution, while the third body possesses a dynamic symmetry plane. The motion of the bodies is described by canonical osculating elements. An expansion in a short Fourier series in canonical osculating Delaunay-Andoyer elements is obtained for the approximate force function of the problem. Theorems for the existence of steady-state solutions are derived, using a modification of the Delaunay-Hill averaging method.

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