Physics
Scientific paper
May 1991
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1991cosre..28..693k&link_type=abstract
Cosmic Res., Vol. 28, No. 6, p. 693 - 703
Physics
Three-Body Problem: Resonances, Satellites: Orbital Evolution
Scientific paper
The spatial rotations of a satellite with respect to the center of mass in the circular three-body problem are discussed in the case of a principal resonance. It is assumed that the orbit of the satellite's motion is described by conditionally-periodic functions of time, and that its central ellipsoid of inertia is almost spherical. It is shown that the averaged equations of motion of a dynamically symmetric satellite can be integrated in quadratures. The action of the gravitational moments causes a slow motion of the angular momentum I2 in Koenig axes - its end describes a drifting loop on a paraboloid of rotation. A classification is given of the possible loops on spatial orbits. It is shown that planar orbits of the satellite correspond to some degeneracy; the loop is deformed into some curve of degree zero. The bifurcations of the stationary motions of the vector I2 are studied, and equations for the critical parameter values, for which the degree of the loop changes, are obtained. The effect of the trajectories of the satellite on its center-of-mass motion is studied.
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