Use of averaging methods in the problem of translational-rotational motion of an axisymmetric body in the gravitational field of a sphere

Details Use of averaging methods in the problem of translational-rotational motion of an axisymmetric body in the gravitational field of a sphere Use of averaging methods in the problem of translational-rotational motion of an axisymmetric body in the gravitational field of a sphere

Aug 1977

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1977mvsfa..18....9b&link_type=abstract

Moskovskii Universitet, Vestnik, Seriia III - Fizika, Astronomiia, vol. 18, July-Aug. 1977, p. 9-16. In Russian.

Astronomy and Astrophysics

Astronomy

1

Axisymmetric Bodies, Equations Of Motion, Gravitational Fields, Orbital Mechanics, Rotating Bodies, Translational Motion, Approximation, Average, Canonical Forms, Celestial Mechanics, Differential Equations, Integral Calculus, Three Dimensional Motion

Scientific paper

The integrability is investigated of various schemes for averaging the differential equations of translational-rotational motion of an axisymmetric body located in the gravitational field of a sphere. The equations of motion are written in canonical Delaunay-type variables. The averaging schemes of Gauss and Moiseev are shown to generate equations that are integrable in the case of three-dimensional motion. It is found that the Fatou and the Delaunay-Hill schemes can be integrated only in the case of two-dimensional translational-rotational motion. A complete system of first integrals is developed for each integrable averaging scheme, and inversion of these first integrals is examined.

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