Astronomy and Astrophysics – Astronomy
Scientific paper
Oct 1977
adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1977mvsfa..18...67b&link_type=abstract
Moskovskii Universitet, Vestnik, Seriia III - Fizika, Astronomiia, vol. 18, Sept.-Oct. 1977, p. 67-74. In Russian.
Astronomy and Astrophysics
Astronomy
2
Orbital Mechanics, Periodic Functions, Poincare Problem, Rotating Bodies, Translational Motion, Two Body Problem, Binary Stars, Eccentricity, Ellipsoids, Equations Of Motion, Orbital Elements, Synchronism
Scientific paper
The existence of an eight-parameter family of periodic Poincare solutions in the problem of planar translational-rotational motion of two solids having a common axis of dynamic symmetry is proved. It is assumed that the centers of inertia of the two bodies describe a planar orbit in a fixed plane. The motion of the bodies is described by canonical osculating elements. By the Poincare method, analytical conditions for the existence of periodic motions of the bodies along orbits of finite eccentricity are obtained. Synchronous translational-rotational motions are investigated for a special case corresponding to two similar ellipsoids.
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